Azimuth angle is the compass direction from which the sunlight is coming. The intersecting line is called the line of no Found inside Page 26This necessitates many azimuth calculations to reduce the granularity of the plot . How to calculate Azimuth Angle using this online calculator? This package was created with Cookiecutter and the audreyr/cookiecutter-pypackage project template. Here, LST is the local solar time in hours. In addition, these devices also allow users to determine appropriate bearings by providing additional reference points such as known local landmarks or even celestial bodies like stars. To convert any given bearing to azimuth, simply subtract it from 360. You can enter a different time zone for a location by selecting Line of sight, azimuth angle bearing and great circle distance calculator. 1. 1:5,000 20" This type of device utilizes basic trigonometry principles to ensure optimal accuracy in the calculations which can greatly simplify navigating uncertain terrain or other scenarios where precise measurements are necessary. Source code is available on GitHub. 0000004442 00000 n 1:10,000 They help provide accurate directions for hiking, camping, sailing and other outdoor activities. In any situation where precise measurements must be taken over great distances, bearing to azimuth calculators provide invaluable assistance. The user simply enters two coordinates (Easting and Northing) for any two points to get the bearing and distance of the vector between them. Save my name, email, and website in this browser for the next time I comment. Click the Pinprick tool on the Production Feature Builder toolbar and click the map. Line of sight, azimuth angle bearing and great circle distance calculator. Calculation of azimuth and solar elevation angle by given the coordinates and time of observation. Excel bearing calculations. For great circles, the result is the azimuth at the starting point of the connecting great circle path. select a city from the pulldown menu, the latitude, longitude and time zone fields Solar tracking is an unaffordable and uncommon option for homeowners and small projects. This calculation can then be used as input for navigating or surveying applications, such as typically found when sailing, hiking, hunting, and other outdoor activities. Bearing / Azimuth Converter. Simple application to convert between bearings and azimuth. From the given azimuth, calculate the bearing of the line. We reviewed their content and use your feedback to keep the quality high. Direction (IV Quadrant): Bearing = 360 - Azimuth. NOT deg/min/sec) Example: The azimuth of the sun at 210 degrees: it is about 2 pm. 001'00" Read more about this calculator. Please note that this web page is the old version of the NOAA Solar Calculator. Step 2: Input the coordinates of two points in the . Revision 95e6c5b0. N45d15'16.7"E) into an azimuth (45.25463867). Making a circular plot of azimuth (degrees on circumfrance) vs time (distance from centre) in python 0 How to display a sprite on the screen in relation to the azimuth What are the drawbacks to solar tube lighting? Compute and tabulate the bearings and azimuths of a regular hexagon. Having good clean lubrication inside helps keep corrosion at bay which can lead to inaccurate readings use bottled oil as directed by manufacturer guidelines when appropriate but also avoid getting water inside always store compasses upside down when passing through waterways (or in airtight container if possible). Note: Since true north is the reference direction most commonly used, all . Simple application to convert between bearings and azimuth. Overwrite the default numbers in the blue boxes below with the latitude or longitude of your location. By knowing the azimuth of the sun, solar time can be calculated. To determine the azimuth and distance of two points on . This calculator is used to add and subtract angles in the form Degrees - Minutes - Seconds (DMS). This application came about when I found my simple CAD program did not accept bearings as input. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Surveyors express angles in several ways. 000'10" standard time. Back when this calculator was first created, we decided to use a non-standard Please, check our dCode Discord community for help requests!NB: for encrypted messages, test our automatic cipher identifier! in these values in the date/time fields. The bearing of a line is measured as an angle from the reference meridian, either the north or the south, and toward the east or the west. 0000055979 00000 n This edition has been reorganized and streamlined to align tightly with current surveying practice, and to teach more rapidly and efficiently. Given a geographic coordinate, an ellipsoidal distance, and a geodetic azimuth, use Vincenty's direct formula to calculate the coordinate of a second point as well as the reverse geodetic azimuth. A press fit bearing, Introduction: What are Preload Pinion Bearings and. our Time Zone Table. The function uses the Great Circle method of calculating distances between two points on the Earth. 0000032731 00000 n Copyright 2020, Keith Sanders IF YOU ARE RUNNING A LOCAL VERSION OF Q-COGO IN MS INTERNET EXPLORER you must first confirm that you wish to allow Q-Cogo run scripts. Calculate the Quadrant field by using the Python code block, as seen below. "South . Physics Since Bearings and Azimuths are both referenced to a meridian it is simple to convert one to the other. The bearing of a line in the direction in which a survey is progressing is called the forward bearing. W = West. Found inside Page 284Components of azimuth angle are stated to 0 : 1 ; for derived true azimuth , only whole degrees are warranted . The user only needs an input such as entering heading elevations, latitudes and longitudes information before being presented with results quickly by the calculator making it ideal for radars when determining bearings quickly from different locations in close vicinity of each other. If angle is less than 0 degrees (e.g. For the rest of you, we encourage you to instead Source code available at GitHub.com. 0000009453 00000 n Taking frequent readings throughout your journey can help identify any swings in readings due to these elements so keep track of them along with any changes made during the course of travel during difficult terrain etcetera, Properly storing and caring for compasses is also important for consistent accuracy over time. Straight angle is the angle at 180 degree. Age Under 20 years old 20 years old level 30 years old level 40 years old level 50 years old level 60 years old level or over Occupation Elementary school/ Junior high-school student 10" Also, bearings must be in azimuth (0 to 360 degrees). Azimuths are used in boundary, topographic, control, and other types of surveys, as well as calculations. Used the Anaconda distribution for development. Fill & Sign Online, Print, Email, Fax, or Download. The program retrieves the current date and time from your computer, and fills Start ArcMap. How to calculate an azimut with 2 points? Just turn on JavaScript in your browser. 1:250,000, Misc: First the quadrant is divided by 2 and the integer portion multiplied by 180. Distance and Bearing Finder. When specifying directions, as is done in the preparation of a property survey, angles may be specified as bearings or azimuths. 0000012646 00000 n 0000007623 00000 n a feedback ? "South 45 East" and "135" are the same direction expressed as a bearing and as an azimuth. acute angle measure less than 90 degrees. 1 sig fig As the atmospheric conditions cannot be modeled precisely the times reported here should be considered correct with an approximation of few minutes. Photo by Denise Jans on Unsplash Mathematics. Or, you can find the single factor you need by Re: Convert Angle (Azimuth) to Bearing format. These techniques will help ensure your readings from your compass are spot-on; if your map skills arent up to snuff then chances are even with a top of the line light weight military compass you wont find your way home easily! So, if used on a worksheet where, say, cell A1 contained your azimuth, then this formula in a cell will return the bearing. By using a bearing to azimuth calculator, you can determine directions such as true north, south east or west. Ham radio tools, bearings and distances calculators category is a curation of 12 web resources on , NS6T's Azimuthal Map, Ham radio digital modes, IOTA Bearing & Distance list for your QTH. See also: Latitude/Longitude Calculator. If all necessary bearings of a traverse are first converted to decimal azimuths, calculations become much easier. . It works by taking the current location and calculating the direction that needs to be traveled in order to reach a specific destination. The actual azimuth is 259.4, 0.3 different from exactly 180 difference. This can be used to place features so they are relative to one another. Follow these steps:Place the notch or center point of your protractor at the point where the sides of the angle meet (the vertex).Place the protractor so that one of the lines of the angle you want to measure reads zero (that's actually 0). Today, the reference plane for an azimuth is typically true north, measured as a 0 azimuth, though other angular units ( grad, mil) can be used. When you want to observe an object such as a comet or planet in the night sky, often you will visit a website that tells you where to look. It starts with North at 0. 2003-2023 Chegg Inc. All rights reserved. What types of applications could benefit from using a Bearing to Azimuth Calculator? Enter the azimuth angle and have the bearing automatically calculated. clear the minutes and seconds fields, or they will be added in.) KawAZ is a Azimuth Angle Calculation Program for the Radio Amateur DX View1.1.5 -- FreeWare. Your browser is currently not running JavaScript. Geography Description of azimuth to bearing converter. 2. or time zone manually, be sure to 6 sig figs, Area: The use of a bearing to azimuth calculator simplifies what otherwise would require complex calculations for directional purposes such as circles, arcs and tangents without having to carry out these calculations manually or rely on inaccurate maps. %PDF-1.3 % If we follow a 60-degree azimuth from magnetic north, we will end up far off to the right of where the Fair Maiden is. E) Compute the angle, smaller than 180, between the bearings in Parts A and B. It also means that you don't have to be connected to the internet to do land survey calculations in Q-Cogo. The practical applications of this tool are numerous; navigators may use it when planning a route, scientists can employ it to track migration patterns, and meteorologists can utilize it to analyze precipitation data on a grand scale. The result will be the difference between the two sets of coordinates in either the specified form of measurement, given as a decimal number with four decimal places. 0.01" az1 = azimuth (10,10,10,40) az1 = 87.3360. Given the first starting direction of side AB: N 34 deg 09 min E, station C is easterly of B. . Cite as source (bibliography): B) Convert 168 ' 44'58" to a bearing. An azimuth is a special kind of geometric angle used chiefly in land navigation. Simple application to convert between bearings and azimuth. There are various types of bearing calculation based on different methods including Cartesian coordinates translations (CST), spherical trigonometry (STD) and pre-calculated look up tables used mainly by navigators when determining distances between two points plus track bearings on marine vessels or aircrafts respectively Both STD & CST method however makes use of sine cosine equations as tools when computing final results regardless whether through manual or automatic means, 5. Many of these applications have the same basic features, so it is a matter of personal preference which one you choose. The shape of the earth. language, literacy and early childhood education, what is connection relationship and networks. 0000001053 00000 n Azimuth tells you what direction to face and Elevation tells you how high up in the sky to look. Bipin Tripathi Kumaon Institute of Technology. So, the best choice was to build a little converter so that values could be copied to the clipboard and pasted into the CAD program. . S 6 6 0 1 3 8 E b. 72 north or less than 72 south, accuracy may be lower due in Results are given in the following units: Equation of Time in minutes of time; Solar Declination in degrees, with positive to the north; Azimuth in degrees clockwise from north; Elevation in degrees up from the horizon; Cosine of . Is a Clone created in a Demiplane native to it? By taking a step-by-step approach, you can more easily see what's going on and how to solve the problem. To acquaint you with the style of compass bearings and units of distance measure, the following explanations and interactive calculators are offered. 0000006264 00000 n The method for doing this varies by browser, but click on your browser's "help" menu to get started. We maintain this page as a courtesy to those people who, for whatever reason, How long can a pianist maintain a repeated, fast figure in one hand? For the north-west quadrant, the bearing must be subtracted from 360 to obtain the azimuth. This is a number from 0 to 360 degrees. The azimuth is a number between 0 and 360, and is an angle (measured clockwise) from due north. b = distance / (Earth Radius) making sure distance and (Earth Radius) are the same units so that we end up with b in . definition of longitude and time zone, to make coordinate entry less awkward. Azimuth Angle is denoted by Az symbol. For each traverse (for next . This form is used in astronomy and defining latitude and longitude. 3. To improve this 'Distance and azimuth between two cities Calculator', please fill in questionnaire. Hectare (Ha) Magnetic declination, sometimes called magnetic variation, is the angle between magnetic north and true north. The latitude of Tokyo is 35.6762 degrees North, while its longitude is 139.6503 degrees East. An azimuth of 180 means you should look south, and so on. Given {lat1, lon1, distance, azimuth} calculate {lat2, lon2}. Get Form. Additionally, it may also be useful in high precision artillery systems and gunnery calculationsas calculating exact distances and angles of fire trajectories are necessary in ensuring safety protocols are followed accordingly. Whether you seek better grades in geography class or need more efficient ways of navigating while exploring new places outside your comfort zone having access to reliable yet easy-to-use measuring devices can make all the difference! 4-4. Most surveyors prefer azimuths to bearings because they are easier to work with, like when calculating traverse data using digital computers. How to calculate an azimut with 2 points? Ask Question Asked 2 years, 10 months ago. Ultimately with its ability aid navigation efforts both on land and at sea, its no wonder why many rely on bearing and azimuth calculators daily so they can accurately find their way around any unfamiliar environments they may encounter during operations. The difference between Azimuth and Bearing is Azimuth uses only angles from 0 to 90 degrees, whereas Bearing uses only 0 to 360 degrees. 0000014061 00000 n No Limit Most internet browsers default to allowing JavaScript unless you make a point of turning it off. To do this, take the protractor reading (60 degrees) and subtract the 10 degrees that magnetic north requires. Prime Meridian. Maintaining. Choosing "Bearing" will use the more traditional quadrantal bearings instead (NE, SE, SW, or NW). calculation can be changed in the same way. Acre (acre), Prec: Is it safe to turn on JavaScript? Forward and Back Bearings. The "Bearings and Azimuths 2.0" app has one primary function. $$\mathrm{S} 66^{\circ} 01^{\prime} 38^{\circ} \mathrm{E}$$ b. See image below for an example of this. . Refer to the image and ensure each item is highlighted appropriately in the Field Calculator window before running the code. If you're struggling to clear up a math equation, try breaking it down into smaller, more manageable pieces. When taking readings off of a compass, it is important to stand straight up with a neutral stanceno leaning or tilting off-balanceso that the direction can be accurately read on the compass dial. When using a bearing to azimuth calculator, users must input the coordinates of their current position as well as that of their desired location in order to generate accurate calculations. 0.1" Write to dCode! Quality is important in all aspects of life. Ans. 1 - To calculate Bearings, Azimuths and Angles in their Degrees, Minutes & Seconds native format. Azimuth is given in degrees from North.This means North is 0 deg, East is 90 deg, South is 180 deg, and West is 270 deg. A Bearing to Azimuth Calculator is an online tool that can be used to calculate the direction of a line between two points or locations on a map, expressed in terms of degrees, or azimuths. Azimuth=Bearing Azimuth=180-Bearing Bearing=Azimuth Bearing=180-Azimuth Quadrant 3: Southwest Quadrant Quadrant 4: Northwest Quadrant Azimuth=180+Bearing Azimuth=360-Bearing Bearing=Azimuth-180 Bearing=360-Azimuth . To perform calculations for a There is no conversion calculator here. I got recommend this and it works really well. The launch azimuth is the angle between north direction and the projection of the initial orbital plane onto the launch location. $$\mathrm{S} 66^{\circ} 02^{\prime} 45^{\circ} \mathrm{E}$$ c. $$\mathrm{S} 23^{\circ} 58^{\prime} 22^{\circ} \mathrm{E}$$ d. $$\mathrm{N} 23^{\circ} 58^{\prime} 22^{\circ} \mathrm{W}$$ 4-5. An azimuth is an angle between 0 and 360 measured clockwise from North. Here is how the Azimuth Angle calculation can be explained with given input values -> 100 = 3.1415926535892-1.3962634015952. 000'30" Positive 90 degrees is facing due west, negative 90 degrees is facing due east. 000'20" So, the best choice was to build a little converter so that values could be copied to the clipboard and pasted into the CAD program. 0000002467 00000 n 1:2,500 0000001267 00000 n Step 4: If you need more than just a general direction, click convert or calculate (depending on whatever tool you are using) for more detailed information about the angle between two points and its associated value in terms of degrees or radians. Azimuth is a specific type of bearing which measures the direction of an object in relation to true north, in the horizontal plane, clockwise from 0 o to 360 o . Example: The azimuth of the sun at 165 degrees: it is around 11 am. With this tool, users enter their starting coordinates (latitude and longitude), their ending coordinates (latitude and longitude), and their desired type of measurement (bearing or azimuth). Introduction to Replacing Wheel Bearings on a Pontiac, Introduction to Polaris Wheel Bearing Grease Welcome, Introduction to Pinion Bearing Removal Tool: What, Introduction to Using a Pilot Bearing Puller from Harbor, Introduction to Installing a Pilot Bearing Installing, How to Use a Bearing to Azimuth Calculator Step by Step, FAQs About Using a Bearing to Azimuth Calculator, Exploring the Benefits of Using a Bearing to Azimuth Calculator, Top 5 Facts About Using a Bearing to Azimuth Calculator, A Comprehensive Guide to Press Fit Bearing Tolerance Charts, Tips for a Smooth Installation of Preload Pinion Bearings, The High Price of Porsche IMS Bearing Replacement: What You Should Know, Everything You Need to Know About Replacing the Wheel Bearings on Your Pontiac G6, The Benefits of Using Polaris Wheel Bearing Grease for Your Vehicle, How to Use a Pinion Bearing Removal Tool to Replace Your Cars Back Axle, The Ultimate Guide to Using a Pilot Bearing Puller from Harbor Freight, A Step-by-Step Guide to Installing a Pilot Bearing in the Right Direction. Due to the many benefits of employing a bearing to azimuth calculator, it has become increasingly popular among those who use navigation systems regularly such as surveyors, boaters, hikers, aviators and more. On the menu bar, click Customize > Toolbars > Production Feature Builder. It is possible for websites to exploit bugs in JavaScript to harm your computer. 0.0001" 0000014039 00000 n Input positive numbers only (e.g. If a Quick and simple equations to estimate these variables are as follows: Here, d is the number of days since January 1st UTC (00:00: hr). 0000001471 00000 n Time of day for the This online calculator is created after the user's request, and it is just a convenient shortcut between Course angle and the distance between the two points on loxodrome (rhumb line). prefer the old calculator. The solar azimuth angle is a way to identify the position of the sun in the sky. An azimuth of 180 means you should look south, and so on. 0.1 Azimuth/Distance calculator - by Don Cross. We can see how dramatic the difference is in the solar azimuth angle for different locations. Selecting "Yes" in the Daylight Saving field will cause the solar position The actual azimuth is 259.4, 0.3 different from exactly 180 difference. N = North. Polynomial (x+2) (x-1) (2x-6) Fraction Multiplication. Mathematics is the science of quantity, structure, space, and change. here a and b represent the two coordinates, and their prefixes are given by: The elevation angles for the other two timings are 49.77 (12:00 noon) and 40.63 (2:00 PM). Calculate the declination, altitude and azimuth angle of the sun in degrees at 8 hours AM on 15 June at a latitude 15 degree in northern hemisphere Box number and item Marks 1 declination (degree) 2 2 Altitude (degree) 2 3 Azimuth (degree) 2. part to the effects of 3 sig figs With the compass in your hand, turn your whole body until the compass needle points to the magnetic declination of + 12 +12\degree + 12. Converting between Azimuths and BearingsQuadrant 1: Northeast quadrant AzimuthBearing BearingAzimuthQuadrant 2: Southeast Quadrant Azimuth180Bearing Bearing180AzimuthQuadrant 3: Southwest Quadrant Azimuth180+Bearing BearingAzimuth180Quadrant. To calculate azimuths about a traverse, it is necessary to obtain the back azimuth of a line. Ninety degrees corresponds to east, 180 degrees is south, 270 degrees is west, and 360 degrees and 0 degrees mark north. What 4 formulas are used for the Bearing Calculator? The input latitudes and longitudes can be scalars or arrays of matching size. Degrees and minutes, e.g. a bug ? Many free-to-use options exist online and some companies even offer paid versions depending on your needs. This activity develops the concept of back azimuths that is, taking an azimuth and proceeding exactly (180 degrees) in the opposite direction. and all data download, script, or API access for "Azimuth" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app! Found insideThe information entered on the worksheet is as follows : Atmospheric Speed Of Sound Calculator and Plotting Diagram AZIMUTH OF INTEREST - Enter the true bearing , in whole degrees , from the point of blast to the point of interest . 0000007645 00000 n So in other words, the azimuth tells you which direction along the horizon you should turn. 4 sig figs The angle is calculated by taking as base/reference the north geographic pole. Step 1: Select a Bearing to Azimuth Calculator. This is read as "34 degrees 24 minutes 16 seconds". Dim strOutput As String. An azimuth bearing indicate direction in degree, north as 0, east 90, south 180, and west 270 (the compass is numbered clockwise from 0 to 360). 0000012624 00000 n An azimuth of 0 means you should look due north. 0000004420 00000 n =az2dms (A1) Note: For your example 134.7454 azimuth, I get a bearing of S4515'17"E instead of your S4515'16"E (one second difference) because I rounded the seconds . Introduction to Bearing and Distance Calculations. First, work backwards (relative to Problem 1A) and find b from the distance by dividing by the Earth radius. select "Enter Lat/Long -->" from the City pulldown box, or your numbers will To use this online calculator for Azimuth Angle, enter Straight Angle (s) & Acute Angle (Aacute) and hit the calculate button. The azimuth is a number between 0 and 360, and is an angle (measured clockwise) from due north. For the north-west quadrant, the bearing must be subtracted from 360 to obtain the azimuth. H|WMo7>X}F:6nQ @{Rg;@#]9$/|$nqf+dV0y86~6{g3. At solar noon, the sun is always directly south in the northern hemisphere and directly north in the southern hemisphere. How to know the time with a compass and azimuth of the sun? I want to be able to type the Azimuth Azimuth: 134.7454 And get the results shown below Bearing: S45d15'16"E I know it might be too much to ask to convert an azimuth to bearing that will show minutes and seconds. In cartography/navigation, an azimuth is the angle (in the plane) formed by the line passing by the 2 points and the line of the two poles. Why does Q-Cogo use JavaScript? The Bearing To Azimuth calculator can prove beneficial in navigating or surveying applications such as sailing, hunting, hiking, etc., where knowing both distances and directions over uneven terrain is crucial informationallowing users to accurately plan ahead according to these measurements. The value 0 indicates north, 90 is east, 180 is south, and 270 is west. The bearing of the line in the direction . An azimuth value of 0 degrees signifies true north, pointing directly towards the geographical North Pole. Please Login or Register to view this content. Urvi Rathod has verified this Calculator and 2100+ more calculators. Great circle azimuth bearing and range calculator (with magnetic north) If you need a BACK BEARING from the distant site back to home do the calculation. Standards: Determine the back azimuth of a given azimuth to the exact degree or mils. Azimuth only measures angles in a clockwise direction, and Bearing can measure angles both clockwise and anticlockwise. Azimuth calculator finds the azimuth from the latitude and longitude . Found inside Page 125741o25'98 , the azimuth of the sun is observed as 016 : 0 pgc . Formula for calculating noon sun angle is: Noon_sun_angle = 90 - Zenith angle. As the compass points with local magnetic fields, declination value is needed to obtain true north.. more. Convert the azimuths from north to bearings, and compute the angles, smaller than 180 between successive azimuths. Proposition 5. First the quadrant is divided by 2 and the integer portion multiplied by 180. atmospheric refraction. These steps should get you started with calculating bearings from one point to another via an online bearing to azimuth calculator! And it is 180 and 270 for the south and west. Bearing is defined as the acute angle formed by measuring the reference meridian from the specified line. A bearing is an angle less than 90 within a quadrant defined by the cardinal directions. Gon) is also supported. In the default example above, if you are in the middle of Trafalgar Square, and your stargazing website has said the object you're looking for can be found at an azimuth of 32°, then you know that to see it, you need to look in the direction of the Coliseum. Viewed 2k times 0.00001", Area: A bearing to azimuth calculator is an invaluable tool for anyone seeking to accurately measure the angle from one point in space to another. No special azimuth formula is needed, just a map, protractor, pencil and your start and end points. This sculpture points directly toward the . 0.025 I have used this to convert latitude and longitude :22.369131978392012,114.11357168108225 to startpoint latitude , longitude :0.39041812966877465,1.991668182365113 with moved distance (in KM) as 0.06574748992919921 Could you please tell me the way to calculate the distance between ? The shortest distance between two points on the surface of a sphere is an arc, not a line. So the azimuth to green is the reference azimuth of 99 degrees, 35 minutes, and 4 seconds plus 180 degrees so that we get the back azimuth of it. This can come in handy if you need an exact measurement for guidance purposes In cartography, for example! NOAA Solar Position Calculator Given the latitude, longitude, and elevation of two points on the Earth, this calculator determines the azimuth (compass direction) and distance of the . In the picture below, the bearing is 40 40\degree 40. 1:25,000 This book will help you unlock all the magic, so you'll be able to use your TI-84 Plus for much more than basic math. 0000001837 00000 n using QGIS 18.16 I am trying to figure out how to cal a reverse azimuth. Direction (III Quadrant): Bearing = Azimuth - 180 Azimuth =Bearing + 180 N.W. From 2 GPS points (Point 1: latitude $lat_1$, longitude $long_1$ and Point 2 latitude $lat_2$, longitude $long_2$), the formula to calculate an azimuth $A$ is $$A = \operatorname{atan2}(y, x)$$ with, $\operatorname{atan2}(y,x) = 2 \arctan \frac{y}{\sqrt{x^2+y^2}+x}$, $x = \cos(lat_1) \times \sin(lat_2) - \sin(lat_1) \times \cos(lat_2) \times \cos(long_2-long_1)$ and $y = \sin(long_2-long_1) \times \cos(lat_2)$.
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