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What is the radian and degree measure?

 

3. Find the radian and degree measure of the angle between the point on the coordinate plane and the x-axis. Show and explain

 

 Mar 13, 2019
edited by Guest  Mar 13, 2019
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Degrees = 60

 

Radians = 1.0472

 

Put these approximate coordinates on a graph paper, and it's easy to say that this point lies on the unit circle. It doesn't give us any degrees, so that makes me think special right triangles. Let's call the point we have P. Draw a perpendicular line to the x axis from P, connect it to the origin, (0, 0) and connect that line to P. Given the coordinates, we can see that one leg is 1/2, and the other is \(\sqrt3/2\) . Time to use Pythagoras, and square both of these numbers. 12/22 + \(\sqrt3^2/2^2\) = c2. This turns out to 1/4 + 3/4 = c2 . So c = 1. Since this side is twice one of the legs,this means that this triangle is a 30-60-90 triangle, so the angle is 60 degrees. To get the radians, I just looked up degrees to radians and that's what it gave me.

 

In case you wanted to check for yourself, formula for unit circle is x 2 + y2 = 1. I couldn't find out how to upload the pic. 

 

Hope this helps!

 Mar 13, 2019

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