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HPC WB4.2 - Evaluating Inverse Trig

Last updated over 5 years ago

6 questions

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Question 1

1.

Find the exact value of each inverse within its range by using the unit circle:

a. \arcsin\left(-\frac{\sqrt{3}}{2}\right)

b. \cos\left(2\sin^{-1}\left( \frac{1}{2} \right)\right)

Question 2

2.

Find the exact value of each inverse within its range by using the unit circle:

a. \csc^{-1}\left( -\sqrt{2} \right)

b. \sin\left( \tan^{-1} \left(-1 \right)\right)

Question 3

3.

Find the exact value of each inverse within its range by using the unit circle:

a. \csc^{-1} \left(-\frac{2\sqrt{3}}{3} \right)

b. \arcsin\left(\cos\left(\frac{\pi}{3}\right)\right)

Question 4

4.

Find the exact value of each inverse within its range by using the unit circle:

a. \sec^{-1}(-2)

b. \arccos\left(\tan\left(\frac{\pi}{4}\right)\right)

Question 5

5.

Find the exact value of each inverse within its range by using the unit circle:

a. \text{arccot}(1)

b. \cos\left(\tan^{-1}\left(\sqrt{3}\right)\right)

Question 6

6.

Find the exact value of each inverse within its range by using the unit circle:

a. \text{arccot}(-1)

b. \tan^{-1}\left(\cos\left(\pi\right)\right)