$$s = 11 \times \frac{315\pi}{180} \approx 60.5 ft$$

$$4600 \times \sin 6^ ext{o} \approx 481 ft$$

$$6 \times \frac{5}{12} \times 2\pi \approx 15.7 in$$

Question 1

Convert $$315^	ext{o} to $$radians.

Accepted Answer

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

Question 2

Convert $$\frac{3\pi}{2}$$ radians to degrees.

Accepted Answer

$$270^	ext{o}$$

Question 3

Find the arc length for a circle with radius $$11 ft $$and central angle $$315^	ext{o}.$$

Accepted Answer

$$s = 11 	imes \frac{315\pi}{180} \approx 60.5 ft$$

Question 4

Which quadrant does the angle $$240^	ext{o}$$ lie in?

Accepted Answer

Quadrant III

Question 5

Find an angle less than $$360^	ext{o}$$ that is coterminal with $$725^	ext{o}.$$

Accepted Answer

$$5^	ext{o}$$

Question 6

Given a right triangle with sides $$a=8$$, $$b=15$$, $$c=17$$, what is $$\sin A$$?

Accepted Answer

$$\frac{8}{17}$$

Question 7

If $$\cos A = \frac{3}{4}$$, what is $$\sin A$$?

Accepted Answer

$$\frac{\sqrt{7}}{4}$$

Question 8

A road is inclined at $$6^	ext{o}. $$After driving $$4600 ft$$, what is the increase in altitude?

Accepted Answer

$$4600 	imes \sin 6^	ext{o} \approx 481 ft$$

Question 9

Let $$	heta be an $$angle in standard position with the point $$(-3,5) on $$its terminal side. What is $$\sin 	heta$$?

Accepted Answer

$$\frac{5}{\sqrt{34}}$$

Question 10

If $$	an 	heta = \frac{5}{12}$$ and $$\sec 	heta \u003c 0$$, what is $$\sin 	heta$$?

Accepted Answer

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

Question 11

What is $$\sin 5\pi$$?

Accepted Answer

$$0$$

Question 12

What is $$	an \frac{5\pi}{6}$$?

Accepted Answer

$$-\frac{1}{\sqrt{3}}$$

Question 13

For the function $$y = -2 \sin(x + \frac{\pi}{2})$$, what is the amplitude?

Accepted Answer

$$2$$

Question 14

For the function $$y = \cos(3x + \pi)$$, what is the period?

Accepted Answer

$$\frac{2\pi}{3}$$

Question 15

What is $$\cos(-\frac{\pi}{4})$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 16

What is the reference angle for $$167^	ext{o}$$?

Accepted Answer

$$13^	ext{o}$$

Question 17

If $$\cos 	heta = \frac{8}{17}$$ and $$	heta is in $$quadrant IV, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{15}{17}$$

Question 18

For the function $$y = \frac{1}{2} \cos(\pi x - 2\pi)$$, what is the vertical shift?

Accepted Answer

$$0$$

Question 19

The minute hand of a clock is $$6$$ inches long and moves from $$12 to$$ $$5 o$$’clock. How far does the tip move?

Accepted Answer

$$6 	imes \frac{5}{12} 	imes 2\pi \approx 15.7 in$$

Arc Length and Unit Circle Study Guide – Trigonometry

Study Guide - Practice Questions