Q: Which of the following is the cofunction identity for $$\sin(\theta)$$?

$$\sin(\theta) = \cos(90^\circ - \theta)$$

Question 1

A Ferris wheel has a radius of 20 meters. If it rotates at a constant angular speed of $$\frac{\pi}{6}$$ radians per minute, what is the linear speed (in meters per minute) of a passenger on the outer edge?

Accepted Answer

$$\frac{20\pi}{6}$$

Question 2

Which of the following angles is an obtuse angle?

Accepted Answer

$$120^\circ$$

Question 3

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

Accepted Answer

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

Question 4

A runner completes a circular track of radius 50 meters in 2 minutes. What is the angular speed in radians per second?

Accepted Answer

$$\frac{\pi}{60}$$

Question 5

Find the length of an arc subtended by a central angle of $$\frac{\pi}{3}$$ radians in a circle of radius 12 cm.

Accepted Answer

$$4\pi$$	ext{ cm}$

Question 6

Which of the following is the cofunction identity for $$\sin(	heta)$$?

Accepted Answer

$$\sin(	heta) = \cos(90^\circ - 	heta)$$

Question 7

Given a point $$(-3, 4) on $$the terminal side of an angle $$	heta$$, what is $$\sin(	heta)$$?

Accepted Answer

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

Question 8

If $$\cos(	heta) = -\frac{1}{2}$$ and $$	heta is in $$quadrant III, what is $$\sin(	heta)$$?

Accepted Answer

$$-\frac{\sqrt{3}}{2}$$

Question 9

What is the reference angle for $$210^\circ$$?

Accepted Answer

$$30^\circ$$

Question 10

Evaluate $$	an(270^\circ).$$

Accepted Answer

Undefined

Question 11

A clock’s minute hand is 15 cm long. How far does the tip travel in 20 minutes?

Accepted Answer

$$10\pi$$	ext{ cm}$

Question 12

Which trigonometric function is even?

Accepted Answer

$$\cos(x)$$

Question 13

If $$\sin(x) = 0.6$$, what is $$\cos(x)$$, given $$x is in $$quadrant I?

Accepted Answer

$$0.8$$

Question 14

Which of the following is a coterminal angle with $$-45^\circ$$?

Accepted Answer

$$315^\circ$$

Question 15

A pendulum swings through an angle of $$\frac{\pi}{4}$$ radians. If the length of the pendulum is 2 meters, what is the length of the arc traced by the pendulum?

Accepted Answer

$$\frac{\pi}{2}$$	ext{ m}$

Question 16

If $$	an(	heta) = 3$$ and $$	heta is in $$quadrant II, what is $$\sin(	heta)$$?

Accepted Answer

$$\frac{3}{\sqrt{10}}$$

Question 17

Which of the following is the periodic property of $$\sin(x)$$?

Accepted Answer

$$\sin(x + 2\pi) = \sin(x)$$

Question 18

If $$\cos(	heta) = 0$$ and $$	heta is $$between $$0^\circ$$ and $$360^\circ$$, which of the following is a possible value for $$	heta$$?

Accepted Answer

$$90^\circ$$

Question 19

A satellite orbits Earth every 90 minutes. If the radius of its orbit is 7000 km, what is its angular speed in radians per minute?

Accepted Answer

$$\frac{2\pi}{90}$$

Trigonometric Functions and Applications: Study Guide for Precalculus

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