Deck 7: The Trigonometric Functions

Question 1

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the given angle:

A) , , is undefined, is undefined, , .
B) , , , , is undefined, is undefined.
C) , , is undefined, is undefined, , .
D) , , , , is undefined, is undefined.
E) , , is undefined, is undefined, , .

Answer 1

, , is undefined, is undefined, , .

Question 2

Rewrite in terms of sine and cosine, and simplify the expression:

A)
B)
C)
D)
E)

Answer 2

Question 3

Rewrite in terms of sine and cosine, and simplify the expression:

A)
B)
C)
D)
E)

Answer 3

Question 4

Use the definition to determine the radian measure of the angle.

A) radians
B) radians
C) radians
D) radians
E) radians

Question 5

Use the definition to determine the radian measure of the angle in the figure below.

A) radians
B) radians
C) radians
D) radians
E) radians

Question 6

Evaluate the expressions using reference angles.

A)
B)
C)
D)
E)

Question 7

Let denote the point where the terminal side of angle (in standard position) meets the unit circle. Use the information to evaluate the six trigonometric functions of . is in Quadrant IV and .

A) , , , , ,
B) , , , , ,
C) , , , , ,
D) , ,
E) , , , , ,

Question 8

Refer to the figure, which shows all of the angles from to that are multiples of or . Relabel the angles in Quadrant III and IV using radian measure.

A)
B)
C)
D)
E)

Question 9

Factor the expression.

A)
B)
C)
D)
E)

Question 10

Factor the expression.

A)
B)
C)
D)
E)

Question 11

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the given angle:

A) , , , , is undefined, is undefined.
B) , , is undefined, is undefined. , .
C) , , , , is undefined, is undefined.
D) , , is undefined, is undefined. , .
E) , , , , is undefined, is undefined.

Question 12

You are given the rate of rotation of a wheel as well as its radius. Determine the following: (a) the angular speed, in units of radians/sec; (b) the linear speed, in units of cm/sec, of a point on the circumference of the wheel; (c) and the linear speed, in cm/sec, of a point halfway between the center of the wheel and the circumference. rpm; cm

A) (a) 156 radian/sec,
(b) 780 cm/sec,
(c) 390 cm/sec
B) (a)
(b) 1,278 cm/sec,
(c) 400 cm/sec
C) (a) radian/sec,
(b) 1,248 cm/sec,
(c) 624 cm/sec
D) (a) 520 radian/sec,
(b) 780 cm/sec,
(c) 1,560 cm/sec
E) (a) radian/sec,
(b) 780 cm/sec,
(c) 390 cm/sec

Question 13

Use a calculator to evaluate , , and for the value of . Round the answers to two decimal places.

A)
B)
C)
D)
E)

Question 14

Refer to the figure, which indicates radian measure on the unit circle for angles in standard position. Use the figure (and the unit circle definitions) to determine whether and are positive or negative.

A) is positive, is positive, is negative
B) is negative, is positive, is negative
C) is positive, is positive, is positive
D) is positive, is negative, is positive
E) is negative, is negative, is positive

Question 15

When a clock reads , what is the radian measure of the (smaller) angle between the hour hand and the minute hand?

A) radians
B) radians
C) radians
D) radians
E) radians

Question 16

Use the figure to approximate the trigonometric values to within successive tenths. Then use a calculator to compute the values to the nearest hundredth. and

A)
B)
C)
D)
E)

Question 17

Refer to the figure, which shows all of the angles from to that are multiples of or . Relabel the angles in Quadrant I and II using radian measure.

A)
B)
C)
D)
E)

Question 18

Evaluate the expressions using reference angles.

A)
B)
C)
D)
E)

Question 19

Use the definitions (not a calculator) to evaluate the six trigonometric functions of the given angle:

A)
B)
C)
D)
E)

Question 20

Match an appropriate value from the right-hand column with each expression in the left-hand column. (a) (A) (b) (B) (c) (C) (d) (D) (E) (F)

A)
B)
C)
D)
E)

Question 21

Simplify the expression and enter the answer in terms of sine and cosine.

A)
B)
C)
D)
E)

Question 22

Suppose that is a right triangle with . If and , find the quantities. .

A) , , , , ,
B) , , , , ,
C) , , , , ,
D) , , , , ,
E) , , , , ,

Question 23

Rewrite in terms of sine and cosine, and simplify the expression:

A)
B)
C)
D)
E)

Question 24

Which of the following is equal to:

A)
B)
C)
D)
E)

Question 25

Which of the following is equal to:

A)
B)
C)
D)
E)