Q: Which of the following is the correct definition of the tangent function in terms of sine and cosine?

$$\tan t = \frac{\sin t}{\cos t}$$

Q: A building casts a shadow of $$172$$ feet when the angle of elevation of the sun is $$\theta. If $$the building is $$125$$ feet tall, what is $$\tan \theta$$?

$$\tan \theta = \frac{125}{172}$$

Question 1

Which of the following best describes an angle in standard position?

Accepted Answer

Its vertex is at the origin and its initial side is along the positive x-axis.

Question 2

What is the radian measure of a central angle that intercepts an arc of length $$s = 12$$ meters on a circle of radius $$r = 4$$ meters?

Accepted Answer

$$	heta = 3$$ radians

Question 3

Which of the following is the definition of one radian?

Accepted Answer

The measure of a central angle that intercepts an arc equal in length to the radius of the circle.

Question 4

Convert $$150^{\circ} to $$radians.

Accepted Answer

$$\frac{5\pi}{6}$$

Question 5

Find a positive coterminal angle for $$-760^{\circ}$$ that is less than $$360^{\circ}.$$

Accepted Answer

$$320^{\circ}$$

Question 6

A Ferris wheel has a radius of $$10$$ meters and rotates at $$0.5$$ revolutions per minute. What is the linear speed of a seat on the Ferris wheel in meters per minute?

Accepted Answer

$$10\pi$$ meters/minute

Question 7

If a point moves along a circle of radius $$r$$ and sweeps out an angle $$	heta in $$time $$t$$, which formula gives the angular speed $$\omega$$?

Accepted Answer

$$\omega = \frac{	heta}{t}$$

Question 8

What is the length of the arc intercepted by a central angle of $$120^{\circ} on a $$circle of radius $$8 cm$$?

Accepted Answer

$$\frac{16\pi}{3} cm$$

Question 9

Which of the following statements about the unit circle is correct?

Accepted Answer

The unit circle has a radius of $$1$$ and its equation is $$x^2$$ + $$y^2 = 1$.

Question 10

If $$\sin t = y$$ and $$\cos t = x$$ for a point $$(x, y) on $$the unit circle, what is the value of $$x^2$$ + $$y^2$$?

Accepted Answer

$$1$$

Question 11

Which of the following is the correct definition of the tangent function in terms of sine and cosine?

Accepted Answer

$$	an t = \frac{\sin t}{\cos t}$$

Question 12

Given a right triangle with sides $$a = 6$$, $$b = 8$$, and hypotenuse $$c = 10$$, what is $$\sin 	heta if$$ $$	heta is $$the angle opposite side $$a$$?

Accepted Answer

$$\frac{6}{10}$$

Question 13

A building casts a shadow of $$172$$ feet when the angle of elevation of the sun is $$	heta. If $$the building is $$125$$ feet tall, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \frac{125}{172}$$

Question 14

Which of the following is the period of the function $$y = \sin(2x)$$?

Accepted Answer

$$\pi$$

Question 15

If $$y = 3\cos\left(\frac{\pi}{2}x\right)$$, what is the amplitude and period of the function?

Accepted Answer

Amplitude: $$3$$, Period: $$\frac{2\pi}{\frac{\pi}{2}} = 4$$

Question 16

Which of the following is true about the graph of $$y = \csc x$$?

Accepted Answer

It has vertical asymptotes at integer multiples of $$\pi.$$

Question 17

If $$\omega is $$the angular speed in radians per second and $$r is $$the radius, what is the formula for linear speed $$v$$?

Accepted Answer

$$v = r\omega$$

Question 18

A point on a circle of radius $$5$$ meters moves through an angle of $$2\pi$$ radians in $$10$$ seconds. What is its linear speed?

Accepted Answer

$$v = \pi$$ meters/second

Chapter 4: Trigonometric Functions and Their Applications

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