Q: What is the domain of $$f(x) = \csc(x)$$?

$$x \neq n\pi$$, where $$n is $$any integer

Question 1

A central angle of a circle measures $$40^\circ$$ and the radius of the circle is 8 cm. What is the area of the sector formed by this angle? (Use $$\pi \approx 3.14$$ and round your answer to two decimal places.)

Accepted Answer

$$22.35\ 	ext{cm}^2$$

Question 2

Convert $$120^\circ to $$radians.

Accepted Answer

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

Question 3

Find the exact value of $$\sin\left(\arccos\left(\dfrac{3}{5}\right)\right). $$

Accepted Answer

$$\dfrac{4}{5}$$

Question 4

A spinning disk has a diameter of 10 inches and rotates at 4 revolutions per second. What is the linear velocity (in inches per second) of a point on the edge of the disk?

Accepted Answer

$$40\pi$$

Question 5

Find the reference angle for $$-200^\circ.$$

Accepted Answer

$$70^\circ$$

Question 6

If $$	an 	heta = -2$$ and $$	heta is in $$quadrant IV, what is the value of $$\sin 	heta$$?

Accepted Answer

$$-\dfrac{2}{\sqrt{5}}$$

Question 7

Given $$f(x) = -3\sin(2x - \pi) + 1$$, what is the amplitude of the function?

Accepted Answer

$$3$$

Question 8

Find the length of the arc intercepted by a central angle of $$200^\circ in a $$circle of radius 35 m. (Round to the nearest meter.)

Accepted Answer

$$122 m$$

Question 9

Which of the following is the period of $$f(x) = 2	an\left(\dfrac{x}{4}ight) - 1$$?

Accepted Answer

$$4\pi$$

Question 10

What is the domain of $$f(x) = \csc(x)$$?

Accepted Answer

$$x 
eq n\pi$$, where $$n is $$any integer

Question 11

Evaluate $$\cos$$^{-1}$$\left(\sin\left(\dfrac{\pi}{2}\right)\right). $$Give your answer in radians.

Accepted Answer

$$0$$

Question 12

If the hypotenuse of a right triangle is $$\sqrt{6}$$ and one leg is $$\sqrt{2}$$, what is the length of the other leg?

Accepted Answer

$$2$$

Question 13

Which of the following is the range of $$f(x) = \arccos(x)$$?

Accepted Answer

$$[0, \pi]$$

Question 14

Find the exact value of $$\sin\left(\arctan\left(\dfrac{3}{4}\right)\right). $$

Accepted Answer

$$\dfrac{3}{5}$$

Question 15

Which of the following transformations occurs in the function $$f(x) = 3\cos(x + 4) - 2$$ compared to $$y = \cos x$$?

Accepted Answer

Vertical stretch by 3, left shift by 4, down shift by 2

Question 16

If $$\sin 	heta = -\dfrac{1}{2}$$ and $$	heta is in $$quadrant III, what is $$	heta in $$degrees?

Accepted Answer

$$210^\circ$$

Question 17

Find the exact value of $$	an\left(\arccos\left(\dfrac{5}{13}ight)ight). $$

Accepted Answer

$$\dfrac{12}{5}$$

Question 18

Which of the following is the correct unit circle value for $$\sin 270^\circ$$?

Accepted Answer

$$-1$$

Question 19

A ladder leans against a wall forming a $$65^\circ$$ angle with the ground. If the foot of the ladder is 5 ft from the wall, how long is the ladder? (Round to the nearest tenth.)

Accepted Answer

$$11.0 ft$$

Precalculus Study Guide: Angles, Trigonometry, and Graphs

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