Question 1

What is the exact value of $$\sin$$^{-1}$$\left( -\frac{\sqrt{2}}{2} \right)$$?

Accepted Answer

$$-\frac{\pi}{4}$$

Question 2

Evaluate $$	an$$^{-1}$$\left( -\frac{\sqrt{3}}{3} ight)$$ exactly.

Accepted Answer

$$-\frac{\pi}{6}$$

Question 3

Find the exact value of $$\cos\left( \sin$$^{-1}$$\left( \frac{1}{2} \right) \right).$$

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 4

If $$\sin$$^{-1}$$(x) is $$defined for $$x \u003e 0$$, express $$\cos(\sin$$^{-1}$$(x)) as an $$algebraic expression in $$x.$$

Accepted Answer

$$\sqrt{1-x^2$}$$

Question 5

Given $$	an$$^{-1}$$(x) is $$defined for $$x \u003e 0$$, write $$\sin(	an$$^{-1}$$(x)) as an $$algebraic expression in $$x.$$

Accepted Answer

$$\frac{x}{\sqrt{1+x^2$}}$$

Question 6

Find the value of $$\cos\left( 	an$$^{-1}$$(\sqrt{3}) ight).$$

Accepted Answer

$$\frac{1}{2}$$

Question 7

Evaluate $$\sec\left( \sin$$^{-1}$$\left( -\frac{\sqrt{2}}{2} \right) \right)$$ exactly.

Accepted Answer

$$\sqrt{2}$$

Question 8

If $$f(x) = \sin^2$ x + \cos^2$ x$$, what is $$f(x)$$ for any real $$x$$?

Accepted Answer

$$1$$

Question 9

Find the value of $$	an$$^{-1}$$(-9)$$ rounded to two decimal places.

Accepted Answer

$$-1.46$$

Question 10

Evaluate $$\sin\left( 	an$$^{-1}$$\left( \frac{5}{12} ight) ight)$$ using a right triangle.

Accepted Answer

$$\frac{5}{13}$$

Question 11

Express $$	an(	an$$^{-1}$$ x) as an $$algebraic expression.

Accepted Answer

$$x$$

Question 12

Find the exact value of $$\sin\left( \cos$$^{-1}$$\left( \frac{3}{5} \right) \right).$$

Accepted Answer

$$\frac{4}{5}$$

Question 13

If $$\cos$$^{-1}$$(x) is $$defined for $$x \u003e 0$$, express $$\sin(\cos$$^{-1}$$(x)) as an $$algebraic expression in $$x.$$

Accepted Answer

$$\sqrt{1-x^2$}$$

Question 14

Evaluate $$\cos\left( 	an$$^{-1}$$\left( \frac{2}{3} ight) ight)$$ using a right triangle.

Accepted Answer

$$\frac{3}{\sqrt{13}}$$

Question 15

Find the value of $$\sin\left( \sin$$^{-1}$$\left( \frac{5}{8} \right) \right).$$

Accepted Answer

$$\frac{5}{8}$$

Question 16

If $$\sin$$^{-1}$$(x) is $$defined for $$x \u003e 0$$, express $$\sec(\sin$$^{-1}$$(x)) as an $$algebraic expression in $$x.$$

Accepted Answer

$$\frac{1}{\sqrt{1-x^2$}}$$

Question 17

Find the value of $$\cos\left( \cos$$^{-1}$$\left( -\frac{3}{5} \right) \right).$$

Accepted Answer

$$-\frac{3}{5}$$

Question 18

Evaluate $$\sin\left( \sin$$^{-1}$$\left( -\frac{\sqrt{2}}{7} \right) \right).$$

Accepted Answer

$$-\frac{\sqrt{2}}{7}$$

Question 19

If $$	an$$^{-1}$$(x) is $$defined for $$x \u003e 0$$, express $$\sec(	an$$^{-1}$$(x)) as an $$algebraic expression in $$x.$$

Accepted Answer

$$\sqrt{1+x^2$}$$

Question 20

Find the value of $$\cos\left( \cos$$^{-1}$$\left( 0.3521 \right) \right)$$ rounded to two decimal places.

Accepted Answer

$$0.35$$

Inverse Trigonometric Functions and Their Applications

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