Question 1

What is the period of the function $$y = -2 	an(3x)$$?

Accepted Answer

$$\dfrac{\pi}{3}$$

Question 2

For the function $$y = \dfrac{1}{4} \cot\left(x - \dfrac{\pi}{2}\right)$$, what are the equations of two consecutive vertical asymptotes?

Accepted Answer

$$x = \dfrac{\pi}{2}$$, $$x = \dfrac{3\pi}{2}$$

Question 3

Solve for $$x in $$the equation $$2\cos^2$ x + 3\cos x + 1 = 0$$ for $$0 \leq x \u003c 2\pi.$$

Accepted Answer

$$x = \pi$$,\ x = 0$

Question 4

Evaluate $$\sin$$^{-1}$$\left(-\dfrac{\sqrt{3}}{2}\right).$$

Accepted Answer

$$-\dfrac{\pi}{3}$$

Question 5

Find $$	an$$^{-1}$$(\sqrt{3}).$$

Accepted Answer

$$\dfrac{\pi}{3}$$

Question 6

Express $$\sin[\cos$$^{-1}$$(u)] as an $$algebraic expression in $$u.$$

Accepted Answer

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

Question 7

Write $$\csc[	an$$^{-1}$$(u)] as an $$algebraic expression in $$u.$$

Accepted Answer

$$\dfrac{\sqrt{1+u^2$}}{u}$$

Question 8

Using the sum identity, evaluate $$\sin(75^\circ).$$

Accepted Answer

$$\dfrac{\sqrt{6} + \sqrt{2}}{4}$$

Question 9

Using the difference identity, evaluate $$\cos(105^\circ).$$

Accepted Answer

$$-\dfrac{\sqrt{6} + \sqrt{2}}{4}$$

Question 10

Using the sum identity, evaluate $$	an(195^\circ).$$

Accepted Answer

$$-2 - \sqrt{3}$$

Question 11

What is the $$x-$$intercept of $$y = -2	an(3x)$$?

Accepted Answer

$$(0, 0)$$

Question 12

Evaluate $$\sin$$^{-1}$$\left(\dfrac{1}{2}\right).$$

Accepted Answer

$$\dfrac{\pi}{6}$$

Question 13

Evaluate $$\cos$$^{-1}$$\left(-\dfrac{1}{2}\right).$$

Accepted Answer

$$\dfrac{2\pi}{3}$$

Question 14

Evaluate $$	an$$^{-1}$$(-1).$$

Accepted Answer

$$-\dfrac{\pi}{4}$$

Question 15

If $$y = \dfrac{1}{4} \cot\left(x - \dfrac{\pi}{2}\right)$$, what is the period of the function?

Accepted Answer

$$\pi$$

Question 16

Evaluate $$\sin$$^{-1}$$(0).$$

Accepted Answer

$$0$$

Question 17

Evaluate $$\cos$$^{-1}$$(0).$$

Accepted Answer

$$\dfrac{\pi}{2}$$

Question 18

Evaluate $$	an$$^{-1}$$(0).$$

Accepted Answer

$$0$$

Question 19

Which of the following is the correct value for $$\sin$$^{-1}$$(1)$$?

Accepted Answer

$$\dfrac{\pi}{2}$$

Trig Exam 2

Guida di studio - Domande di pratica