Find the exact values of the inverse trigonometric functions on the unit circle
Answer 1
Chloe Evans
Consider the point $P(-\frac{1}{2}, -\frac{\sqrt{3}}{2})$ on the unit circle. Determine the exact values for the following inverse trigonometric functions:
1. $\arcsin(-\frac{\sqrt{3}}{2})$
2. $\arccos(-\frac{1}{2})$
3. $\arctan(\frac{\sqrt{3}}{3})$
Answer:
1. $\arcsin(-\frac{\sqrt{3}}{2}) = -\frac{\pi}{3}$
2. $\arccos(-\frac{1}{2}) = \frac{2\pi}{3}$
3. $\arctan(\frac{\sqrt{3}}{3}) = \frac{\pi}{6}$
Answer 2
Ella Lewis
Given the point $P(-frac{1}{2}, -frac{sqrt{3}}{2})$ on the unit circle, compute the exact values for the following:
1. $arcsin(-frac{sqrt{3}}{2})$
2. $arccos(-frac{1}{2})$
Answer:
1. $arcsin(-frac{sqrt{3}}{2}) = -frac{pi}{3}$
2. $arccos(-frac{1}{2}) = frac{2pi}{3}$
Answer 3
Lucas Brown
For the point $P(-frac{1}{2}, -frac{sqrt{3}}{2})$ on the unit circle, find:
1. $arcsin(-frac{sqrt{3}}{2}) = -frac{pi}{3}$
2. $arccos(-frac{1}{2}) = frac{2pi}{3}$
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