When do i need to use radians

Revision December 7, The inequality above is derived this way. Consider the unit circle shown below. The central angle is and the coordinates of A are. Then the area of triangle OAB is. The area of sector. By similar triangles. Then the area of This is larger than the area of the sector, which establishes the inequality above.

Multiply the inequality by and take the reciprocal to obtain. Finally, take the limit of these expression as and the limit is established by the squeeze theorem.

Thank you so much for this article. In Surveying, we use the Whole Circle Bearing WCB or Polar Coordinates, for all of our traverse calculations and convert that to rectangular coordinates to get the precise location of a point. But, I seem to keep falling short of the exact way in which the two work together to create the rectangular coordinate. Using the following sample numbers: Distance: Taking just the portion of the equations: COS Like Like.

Drop a perpendicular from the point to the x-axis. This forms a right triangle with hypotenuse of r. By right triangle trigonometry the length of this segment is and the distance from the pole to the foot of the perpendicular is. These same equations work for points in other quadrants and for angles with a negative measure i. Calculations may be done in degrees or radians as long as the calculator or computer you are using is set in the proper mode.

If your calculator or computer is set for degrees, there is no need to convert to radians. If your angles are measured in degrees, use degree mode on your device. If your distance is Your examples are correct, but unduly long.

There is no need to do things step by step; any calculator or computer or spreadsheet will do the work for you. That is, there is no need to change back and forth between degrees and radians. With your calculator in degree mode: and. With your calculator in radian mode enter and. Either way, the point in polar form I hope this answers your questions. If not, write again. BTW I worked for my four years in college for a land surveyor.

Work I very much enjoyed. Of course, back then we used optical transits theodolites reading the angles with a vernier scale and measured distance with a steel tape.

Hello Lin, Thank you so very much for your fantastic reply. That was quite fun to do. Baron Apparently Excel is set to work in radians. Leveling rods: I remember them. Real Of course by then our steel chains were feet, marked in decimal feet, not inches — some improvement.

You can buy real 66 foot chains on Ebay! I disagree with having the inequality with equal sign. Another approach is to graph sin x and x separately.

It seems to me that there might be more fundamental problem than typing a value into calculator. Show 6 more comments. Active Oldest Votes. If there is no degree symbol, then use radian mode.

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The unofficial elections nomination post. Email Address. Skip to content. Home About Faq. Q: Can a human being survive in the fourth dimension? Q: Why radians? Posted on October 30, by The Physicist. Physicist : Because calculus. To see why you have to get to know the unit circle.

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