Trigonometric Values and Distance Around a Unit Circle

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1. Given that sin 59.1 =0.8581, cos 59.1 =0.5135 and tan 59.1=1.6709, find the six function values for 30.9.
30.9° + 59.1° = 90°
So the two angles are complementary angles.
Therefore,

2. If I start at (0,1) on the unit circle, and I travel around the circle until I come to
(square root of -3/2, -1/2) how far (distance) have I traveled around the circle.

So you start from A and travel counter-clockwise to reach B, which is the third quadrant.
We can convert the xy coordinates to the polar coordinates.
For B

Since you are on the unit circle, so r = 1,
Then

With in the third quadrant, we have
Then the arc length (the distance you traveled is)

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