Q: Which of the following is the correct definition of $$\cot \theta in a $$right triangle?

$$\frac{\text{adjacent}}{\text{opposite}}$$

Question 1

Convert $$135^\circ to $$radians.

Accepted Answer

$$\frac{3\pi}{4}$$ radians$

Question 2

Which of the following is the correct formula to convert radians to degrees?

Accepted Answer

Multiply radians by $$\frac{180^\circ}{\pi}$$

Question 3

Given a point $$P = (x, y) on $$the unit circle corresponding to $$t$$, what is $$	an t in $$terms of $$x$$ and $$y$$?

Accepted Answer

$$\frac{y}{x}$$

Question 4

If $$\sin t = y$$ and $$\cos t = x$$ for a point on the unit circle, what is $$\csc t$$?

Accepted Answer

$$\frac{1}{y}$$

Question 5

A right triangle has sides $$a = 5$$, $$b = 12. $$What is the length of the hypotenuse $$c$$?

Accepted Answer

$$c = 13$$

Question 6

For the triangle in the previous question, what is $$\sin 	heta$$?

Accepted Answer

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

Question 7

What is the amplitude and period of $$y = 3 \sin 2x$$?

Accepted Answer

Amplitude: $$3$$, Period: $$\pi$$

Question 8

Which of the following best describes the period of $$y = 	an x$$?

Accepted Answer

$$\pi$$

Question 9

What is the domain of $$y = \csc x$$?

Accepted Answer

All real numbers except integral multiples of $$\pi$$

Question 10

A surveyor stands 125 feet from the base of a tower. The angle of elevation to the top is $$57.2^\circ. $$What is the height of the tower to the nearest foot?

Accepted Answer

188 ft

Question 11

Given $$y = 4 \cos 2\pi x$$, what is the period of the function?

Accepted Answer

$$1$$

Question 12

Which trigonometric function is even?

Accepted Answer

$$\sec x$$

Question 13

What is the range of $$y = \sec x$$?

Accepted Answer

$$y \leq -1 or$$ $$y \geq 1$$

Question 14

If $$y = -2 \sin \frac{\pi}{4}x$$, what is the amplitude and period?

Accepted Answer

Amplitude: $$2$$, Period: $$8$$

Question 15

Which of the following is the correct definition of $$\cot 	heta in a $$right triangle?

Accepted Answer

$$\frac{	ext{adjacent}}{	ext{opposite}}$$

Question 16

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

Accepted Answer

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

Question 17

For the function $$y = 2 \cot x$$, what is its period?

Accepted Answer

$$\pi$$

Question 18

If $$y = 3 \sec x$$, what is the range of $$y$$?

Accepted Answer

$$y \leq -3 or$$ $$y \geq 3$$

Question 19

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

Accepted Answer

$$\frac{\pi}{3}$$

Question 20

Given $$y = 2 \sin \frac{1}{4}x$$, what is the period?

Accepted Answer

$$8$$

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