Suppose A is the arc on the unit circle that connects (1,0)(1,0) to (-12/13, 5/13)(1213,513) and passes through (0,-1)(0,1). Let uu be the measure of the angle that subtends this arc. Find the value of sin(u)sin(u)?

1 Answer
Feb 26, 2018

See below.

Explanation:

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If we pass through point (0,-1)(0,1) then we are rotating in a anti clockwise direction.

We can see by the coordinates (-12/13,5/13)(1213,513) that the terminal side is in the II quadrant. The yy coordinate 5/13513 is the sine ratio for the angle that is formed with the negative xx axis, which will be arcsin(5/13)arcsin(513), but we have rotated through the IV and III quadrants, so our angle bbuu will be -arcsin(5/13)-pi~~-3.536383774color(white)(8888)arcsin(513)π3.5363837748888radians or -202.62^@202.62.

I have given the angle as a negative rotation, but in angles subtended by arcs this is usually given as a positive angle .i.e. 3.536383773.53638377 radians.

sin(u)=sin(-arcsin(5/13)-pi)~~0.3846153846sin(u)=sin(arcsin(513)π)0.3846153846