Quiz about Precalculus 3.1 – 3.3 Quiz Review

Question 1

The amplitude of a periodic function is 4.5 units and the maximum value of the function is 6. What is the minimum value of the function?

Accepted Answer

-3

Answer

1.5

Answer

9

Answer

-4.5

Question 2

A periodic function goes through 12 cycles in 7 minutes. What is the period of one cycle in seconds?

Accepted Answer

35 seconds

Answer

42 seconds

Answer

30 seconds

Answer

28 seconds

Question 3

For the periodic function, a portion of the graph is shown below. Given that f(-3) = -2, find the value of the period, k. It is known, for any integer value of n, that f(x + nk) = f(-3). What is the ordered pair on the graph of f when n = 2?

Accepted Answer

k = 12; f(21) = -2

Answer

k = 10; f(18) = -3

Answer

k = 12; f(27) = -2

Answer

k = 10; f(-22) = -3

Question 4

Find the point (x, y) on the unit circle that corresponds to the real number $$t=\frac{8\pi}{3}$$ .

Accepted Answer

$$\left(-\frac{1}{2},\frac{\sqrt{3}}{2}\right)$$

Answer

$$\left(-\frac{\sqrt{3}}{2},\frac{1}{2}\right)$$

Answer

$$\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$$

Answer

$$\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$$

Question 5

The figure shows a circle centered at the origin with an angle of measure $$ heta$$ radians in standard position. The coordinates of P are (x, -y) where the terminal ray of the angle intersects the circle. Which of the following statements is true about the cosine of $$ heta$$ ?

Accepted Answer

C. $$\cos heta = \frac{x}{4}$$ because it is the ratio of the horizontal displacement of P from the y-axis to the distance between the origin and P.

Answer

A. $$\cos heta = \frac{y}{4}$$ because it is the ratio of the vertical displacement of P from the y-axis to the distance between the origin and P.

Answer

B. $$\cos heta = -\frac{y}{4}$$ because it is the ratio of the vertical displacement of P from the y-axis to the distance between the origin and P.

Answer

D. $$\cos heta = -\frac{x}{4}$$ because it is the ratio of the horizontal displacement of P from the y-axis to the distance between the origin and P.

Question 6

If $$\sin heta < 0$$ and $$\cos heta = \frac{4}{9}$$ , find tangent of $$ heta$$ and the coordinates of point P = (x, y).

Accepted Answer

$$ an heta=-\frac{\sqrt{65}}{4};\ p=\left(4,-\sqrt{65} ight)$$ ;

Answer

$$ an heta=-\frac{9}{4},\ p\ =\ \left(4,-9 ight)$$

Answer

$$ an heta=-\frac{\sqrt{65}}{9},\ p\ =\ \left(9,-\sqrt{65} ight)$$

Answer

$$ an heta=\frac{\sqrt{65}}{3},\ p=\left(4,\sqrt{65} ight)$$

Question 7

A portion of the periodic function y = g(x) is shown above. Use this graph to analyze the function and complete the following. State the amplitude the period, and midline for y = g(x).

Accepted Answer

amplitude: 4, period: 12, midline: y = 1

Answer

amplitude: 8, period: 12, midline: y = 1

Answer

amplitude: 8, period: 6, midline: y = 2

Answer

amplitude: 5, period: 12, midline: y = 1

Question 8

If $$\sin heta = -\frac{5}{8}$$ and $$\pi \leq heta \leq \frac{3\pi}{2}$$ , find $$ an heta$$ .

Accepted Answer

$$\frac{5}{\sqrt{39}}$$

Answer

$$\frac{\sqrt{39}}{8}$$

Answer

$$\frac{\sqrt{39}}{5}$$

Answer

$$-\frac{5}{\sqrt{89}}$$

Question 9

An airplane leaves the runway climbing at an angle of $$ heta = \frac{\pi}{10}$$ and with a speed of 255 feet per second. Find the altitude of the plane after 3 minutes. Round your answer to the nearest tenth.

Accepted Answer

14,183.9 feet

Answer

4728.0 feet

Answer

13,905.7 feet

Answer

12,196.4 feet

Question 10

Given an angle $$ heta = \frac{7\pi}{12}$$ , in standard position, and the radius $$r = 8$$ , centered at the origin, find the coordinates of point $$P = (x, y)$$ of the angle where the terminal ray intersects the circle.

Accepted Answer

(-2.07, 7.73)

Answer

(7.73, -2.07)

Answer

(2.07, -7.73)

Answer

(30.92, -8.28)

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