Q: Which of the following is the correct definition of the secant function in terms of the unit circle?

$$\sec \theta = \frac{1}{\cos \theta}$$

Q: Which of the following is the correct domain of the function $$f(x) = \cot x$$?

$$x \neq n\pi$$, \ n \in \mathbb{Z}$

Question 1

A Ferris wheel with a radius of 20 meters completes one full revolution every 60 seconds. If a passenger starts at the lowest point, which of the following equations best models the passenger's height $$h (in $$meters) above the ground as a function of time $$t (in $$seconds), assuming the center of the wheel is 22 meters above the ground?

Accepted Answer

$$h(t) = 20 \sin\left(\frac{\pi}{30} t - \frac{\pi}{2}\right) + 22$$

Question 2

Which of the following is the correct definition of the secant function in terms of the unit circle?

Accepted Answer

$$\sec 	heta = \frac{1}{\cos 	heta}$$

Question 3

Convert $$225^\circ to $$radians.

Accepted Answer

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

Question 4

If $$	an 	heta = 3$$ and $$	heta is in $$the second quadrant, what is $$\sin 	heta$$?

Accepted Answer

Question 5

Which of the following is the correct domain of the function $$f(x) = \cot x$$?

Accepted Answer

$$x 
eq n\pi$$, \ n \in \mathbb{Z}$

Question 6

A sound wave can be modeled by $$y = 0.5 \sin(440\pi t)$$, where $$t is in $$seconds. What is the frequency of the wave in Hz?

Accepted Answer

$$220$$

Question 7

Which of the following is the correct range of the function $$f(x) = \sec x$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 8

If $$\sin 	heta = -\frac{1}{2}$$ and $$	heta is in $$the fourth quadrant, what is $$	heta in $$radians?

Accepted Answer

$$\frac{11\pi}{6}$$

Question 9

Which of the following is the correct formula for the period of the function $$f(x) = a \sin(bx + c) + d$$?

Accepted Answer

$$\frac{2\pi}{b}$$

Question 10

Evaluate $$\arccos\left(\frac{1}{2}\right).$$

Accepted Answer

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

Question 11

A point on the unit circle has coordinates $$\left(\frac{3}{5}, y\right)$$, where $$y \u003e 0. $$What is the value of $$y$$?

Accepted Answer

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

Question 12

Which of the following statements about the inverse sine function $$y = \arcsin x is $$true?

Accepted Answer

Its domain is $$[-1, 1]$$ and its range is $$\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$

Question 13

If $$	an 	heta = -1$$ and $$	heta is in $$the fourth quadrant, what is $$	heta in $$radians?

Accepted Answer

$$\frac{7\pi}{4}$$

Question 14

Which of the following is the correct identity for $$\cot x in $$terms of sine and cosine?

Accepted Answer

$$\cot x = \frac{\cos x}{\sin x}$$

Question 15

A pendulum swings according to the equation $$	heta(t) = 0.2 \cos(\pi t)$$, where $$	heta is in $$radians and $$t is in $$seconds. What is the maximum angular displacement?

Accepted Answer

$$0.2$$ radians

Question 16

Which of the following is the correct period of the function $$f(x) = 	an x$$?

Accepted Answer

$$\pi$$

Question 17

If $$\csc 	heta = 2$$ and $$	heta is in $$the first quadrant, what is $$\sin 	heta$$?

Accepted Answer

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

Question 18

Which of the following is the correct amplitude of the function $$f(x) = 3 \sin(2x) - 4$$?

Accepted Answer

$$3$$

Question 19

A circular track has a radius of 50 meters. What is the length of the arc subtended by a central angle of $$72^\circ$$?

Accepted Answer

$$62.8$$ meters

Question 20

Which of the following is the correct value of $$\sin$$^{-1}$$(0)$$?

Accepted Answer

$$0$$

Precalculus Study Notes: Trigonometric and Circular Functions

Guida di studio - Domande di pratica

Study guide - Flashcard