Deck 8: The Trigonometric Functions

Question 1

Convert the given angle to degree measure.

Answer 1

810°

Question 2

Convert the given angle to degree measure.
760°

Answer 2

Question 3

Convert the given angle to degree measure.
-55°

Answer 3

-

Question 4

Convert the given angle to degree measure.
6°

Question 5

Which of the following angles could represent the angle - ?

A)
B)
C)
D) none of these

Question 6

Give the values of sin t and cos t, where t is the radian measure of the angle shown. Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.

Question 7

Which of the following statements is false?

A) The terminal side of the angle θ = - lies in the fourth quadrant.
B) The terminal side of the angle θ = lies in the first quadrant.
C) The degree measure of θ = is 390°.
D) The degree measure of θ = - is 135°.

Question 8

Convert the given angle to degree measure.
10°

Question 9

Convert the given angle to degree measure.
780°

Question 10

Convert the given angle to degree measure.
-

Question 11

Convert -150° to radian measure.

A) $\frac { 7 } { 6 }$
B) $\frac { 5 } { 3 }$
C) - $\frac { 5 } { 6 }$ π
D) - $\frac { 5 } { 3 }$ π
E) none of these

Question 12

Convert the given angle to degree measure.
15°

Question 13

Convert the given angle to degree measure.
-210°

Question 14

Convert the given angle to degree measure.

Question 15

Give the value of sin t where t is the radian measure of the angle shown.

A) =
B) 2
C) - = -1
D) -2
E) none of these

Question 16

Convert the given angle to degree measure.

Question 17

Convert the given angle to degree measure.
-3π

Question 18

Convert the given angle to degree measure.

Question 19

Convert 327° to radian measure.

A) $\frac { 109 } { 60 }$
B) $\frac { 109 \pi } { 120 }$
C) $\frac { 109 \pi } { 60 }$
D) $\frac { 109 } { 120 }$

Question 20

Does this represent an angle of - radians?

Question 21

Find t such that 0 ≤ t ≤ π and cos t = cos .
Enter just a reduced quotient of form with π in the numerator (unlabeled).

Question 22

Give the values of sin t and cos t, where t is the radian measure of the angle shown. Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.

Question 23

Differentiate.
(sin

A) 7(sin cos x
B) 7
C) 7
D) 7 sin x

Question 24

Differentiate.
sin

A) 5 cos
B) 5 cos x
C) 5 sin
D) 5x cos

Question 25

Differentiate.
sin

A) 3x( + cos )
B) (sin + cos )
C) 3 ( + cos )
D) 3 (sin + cos )

Question 26

Find t such that - ≤ t ≤ and sin t = sin .

A)
B)
C)
D) -
E) none of these

Question 27

Determine the value of cos t when t = -7π.

A) -1
B) -2
C) 1
D) $\frac { \sqrt { 2 } } { 2 }$
E) none of these

Question 28

Differentiate.
sin

A) cos
B)
C) 4 sin
D) sin

Question 29

Find t such that 0 ≤ t ≤ π and cos t = cos .
Enter just a reduced quotient of form with π in the numerator (unlabeled).

Question 30

Find the t such that 0 ≤ t ≤ π and cos t = cos $\left( - \frac { 2 \pi } { 3 } \right)$ .

A) $\frac { \pi } { 3 }$
B) - $\frac { \pi } { 3 }$
C) $\frac { 2 \pi } { 3 }$
D) $\frac { \pi } { 6 }$
E) none of these

Question 31

Find t such that 0 ≤ t ≤ and sin t = cos t.

A) 0
B)
C)
D)
E) none of these

Question 32

Differentiate.

A)
B)
C) -
D) 1

Question 33

Refer to the triangle whose sides and angles are labeled below. Estimate t if a = 24, b = 10, and c = 26. Enter just a real number rounded to one decimal place.

Question 34

Determine the value of sin t and cos t when t = 3π.
Enter your answer as just a, b where a represents sin t and b represents cos t (no labels)

Question 35

Determine the value of sin t when t = $\frac { 11 \pi } { 2 }$ .

A) 1
B) $\frac { 1 } { 2 }$
C) -1
D) 0
E) none of these

Question 36

Refer to the triangle whose sides and angles are labeled below. If t = 0.5 and a = 5, find c. Enter just a real number rounded to one decimal place (unlabeled).

Question 37

Find t such that - ≤ t ≤ and sin t = sin .
Enter just a reduced quotient of form with π in the numerator (unlabeled).

Question 38

Differentiate.

A) 6 sin 3t cos 3t
B) 6 sin 3t
C) 2 sin 3t cos 3t
D) 2 sin 3t
E) none of these

Question 39

Refer to the triangle whose sides and angles are labeled below. If t = 0.6 and a = 4.1, find b. Enter just a real number rounded to one decimal place (unlabeled).

Question 40

Suppose sin t = - and cos t is negative. What is cos t?

A) -
B)
C) -
D)
E) none of these

Question 41

sin x cos 3x
Enter cosine terms first, no parentheses around arguments.

Question 42

2 (4t)Enter cosine terms before sine terms, no parentheses around arguments.

Question 43

Differentiate.
x sin x

Question 44

( )Enter sine terms before cosine terms with parentheses around arguments.

Question 45

x x
Enter cosine before sine in all terms, no parentheses around the arguments.

Question 46

Differentiate.
cos 2t cos 3t

A) -sin 2t cos 3t - cos 2t sin 3t
B) 2sin 2t cos 3t + 3cos 2t sin 3t
C) -2sin 2t cos 3t - 3cos 2t sin 3t
D) none of these

Question 47

(x + 4)Enter cosines before sines with parentheses around arguments.

Question 48

6x (sin x)Enter cosines before sines in terms using parentheses around arguments.

Question 49

ln(1 + sin x)Enter a quotient of sine and cosine functions without parentheses around their arguments.

Question 50

sin Enter your answer in the form P(x) ∙(sinR(x) ± cosS(x)) where P, Q, R, S are polynomials in x in standard form. No parentheses around the arguments of sine and cosine.

Question 51

Enter cosine before sine (except in the given exponential) and use parentheses around arguments.

Question 52

cos(cos x)Enter sines before cosines with parentheses around arguments and a multiplication dot between the first two terms.

Question 53

3 cos x sin 2x
Enter cosine terms first, no parentheses around arguments.

Question 54

Enter a quotient of sine functions without parentheses around the arguments of sine.

Question 55

Differentiate.

A) cos x
B)
C) cos x - sin x
D) none of these

Question 56

(3t)Enter sines before cosines with parentheses around arguments.

Question 57

sin Do not enter parentheses around arguments.

Question 58

Differentiate.
sin 3 Do not enter parentheses around arguments.

Question 59

Differentiate.
sin 3x
No parentheses around arguments.

Question 60

ln(sin 3t)Enter a quotient in terms of cosine and sine, no parentheses around arguments.

Question 61

Find the equation of the tangent line tangent to the graph of y = cos 3x + 2 sin x at x = .
Enter your answer in standard point-slope form.

Question 62

Find the indefinite integral.
Enter your answer without parentheses.

Question 63

Find the slope of the line tangent to the graph of y = sin 2t at t = .
Enter just an integer.

Question 64

Find the indefinite integral.

A) - cos 2t + C
B) -cos t + C
C) - cos t + C
D) -2 cos 2t + C

Question 65

Find the indefinite integral.
dx

A) -cos (2x + 1) + C
B) sin(2x + 1) + C
C) sin (2x + 1) + C
D) 2cos (2x + 1) + C
E) none of these

Question 66

Find the indefinite integral.
Enter your answer using parentheses around the argument of the function.

Question 67

Find the indefinite integral.
Enter your answer without parentheses around the argument of the function.

Question 68

Find the indefinite integral.
dx

A) sin (π - 3x) + C
B) - sin (π - 3x) + C
C) 3 cos (π- 3x) + C
D) -sin (π - 3x) + C
E) none of these

Question 69

Find the slope of the line tangent to the graph of y = 4t at t = .
Enter just a .

Question 70

Find the indefinite integral.
Enter your answer without parentheses.

Question 71

Find the indefinite integral.
Enter your answer using parentheses around the argument of the function.

Question 72

Find the equation of the line tangent to the graph of y = sin 2x at x = ?

A) y = -2x - π
B) y = -
C) y = (cos 2x)
D) y - 1 = x -
E) none of these

Question 73

Find the tangent line to the graph of f(x) = at .

A) y = 8
B) y = x - 8
C) y = x - 8
D) y = -8
E) none of these

Question 74

Find the indefinite integral.

A) sin x - cos x + C
B) 2cos x + C
C) cos x - sin x + C
D) 2sin x + C
E) none of these

Question 75

Find the slope of the tangent line to the graph of y = cos at the origin.
Enter just an integer.

Question 76

Find the indefinite integral.

A) 3 cos(t - π) + C
B) -3 cos t + C
C) -3 cos(t - π) + C
D) 3π cos(t - π) + C
E) none of these

Question 77

Find the tangent line to the graph of f(x) = sin x + cos x at (π, -1).

A) y = π
B) y = -x + π -1
C) y = x + π
D) y = -x + 1
E) none of these

Question 78

Find the indefinite integral.
Enter your answer in terms of cosine without using parentheses.

Question 79

Find the slope of the line tangent to the graph of y = sin $\left( \frac { \pi } { 2 } - x \right)$ - cos x at x =
$\frac { \pi } { 4 }$ .

A) $\frac { 1 } { 2 }$
B) 0
C) $\frac { \sqrt { 2 } } { 2 }$
D) $\sqrt { 2 }$

Question 80

Find the tangent line to the graph of f(x) = 2x at .

A) 2
B) -2
C) -1
D) 1
E) none of these