Deck 15: Trigonometric Functions Web

Question 1

Solve the triangle for the indicated side and angle.

A) $\begin{array} { l l } \text { angle } \theta : & 30 ^ { \circ } \\\text { side } c : & 10\end{array}$
B) $\begin{array} { l l } \text { angle } \theta : & 60 ^ { \circ } \\\text { side } c : & 10\end{array}$
C) angle $\theta : 30 ^ { \circ }$
side $c$ : $\quad 4 \sqrt { 2 }$
D) $\begin{array} { l l } \text { angle } \theta : & 35 ^ { \circ } \\\text { side } c : & 4 \sqrt { 2 }\end{array}$
E) angle $\theta : 50 ^ { \circ }$
side $c : \quad 10$

Answer 1

$\begin{array} { l l } \text { angle } \theta : & 60 ^ { \circ } \\\text { side } c : & 10\end{array}$

Question 2

Find the radian measure of the given angle. 225o

A) $\frac { 5 \pi } { 2 }$
B) $\frac { 15 \pi } { 4 }$
C) $\frac { 45 \pi } { 4 }$
D) $\frac { 5 \pi } { 4 }$
E) $\frac { 5 \pi } { 8 }$

Answer 2

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

Question 3

A guy wire is stretched from a broadcasting tower at a point 300 feet above the ground to an anchor 175 feet from the base (see figure). How long is the wire?

A)347.31 feet
B)173.66 feet
C)243.67 feet
D)121.83 feet
E)237.50 feet

Answer 3

347.31 feet

Question 4

Find $\sin \theta$ given that $\sec \theta = 4$ and $0 < \theta < \frac { \pi } { 2 }$ .

A) $4$
B) $\sqrt { 15 }$
C) $\frac { \sqrt { 15 } } { 4 }$
D) $\frac { 1 } { \sqrt { 15 } }$
E) $\frac { 1 } { 16 }$

Question 5

From the given function $\cos \theta = \frac { 4 } { 5 }$ , find the following trigonometric function. $\sin \theta$

A) $\frac { 5 } { 3 }$
B) $\frac { 5 } { 4 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 4 } { 5 }$
E) $\frac { 3 } { 9 }$

Question 6

Evaluate without using a calculator, leaving the answers in exact form. $\sin \frac { 3 \pi } { 4 }$

A) $\frac { \sqrt { 2 } } { 2 }$
B) $\frac { 1 } { 2 }$
C)1
D)0
E) $\frac { 3 } { 2 }$

Question 7

Determine two coterminal angles (one positive and one negative) for each angle. Give the answers in radians.

A) positive: $\frac { 19 \pi } { 9 }$

negative: $\frac { 37 \pi } { 19 }$
B) positive: $\quad - \frac { 35 \pi } { 18 }$

negative: $\frac { 37 \pi } { 18 }$
C) positive: $\quad - \frac { 37 \pi } { 18 }$

negative: $\frac { 35 \pi } { 18 }$
D) positive: $\frac { 37 \pi } { 18 }$

negative: $\quad - \frac { 35 \pi } { 18 }$
E) positive: $\frac { 37 \pi } { 19 }$

negative: $\quad - \frac { 35 \pi } { 17 }$

Question 8

Find the cosine of $$\theta$$ .

A) $- \frac { 5 } { 12 }$
B) $- \frac { 13 } { 12 }$
C) $\frac { 13 } { 5 }$
D) $- \frac { 12 } { 13 }$
E) $\frac { 5 } { 13 }$

Question 9

Find the cosine of $\theta$ .

A) $\frac { 8 } { 17 }$
B) $\frac { 8 } { 15 }$
C) $\frac { 15 } { 17 }$
D) $\frac { 17 } { 8 }$
E) $\frac { 17 } { 15 }$

Question 10

Evaluate without using a calculator. $\tan \frac { \pi } { 4 }$

A) $1$
B) $\text { undefined }$
C) $\frac { \sqrt { 3 } } { 2 }$
D) $\frac { \sqrt { 2 } } { 3 }$
E)0

Question 11

Find the area of the equilateral triangle with sides of length $s = 18$ in. Round your answer to two decimal places.

A)121.50 square inches
B)561.18 square inches
C)140.30 square inches
D)162.00 square inches
E)486.00 square inches

Question 12

Find the radian measure of the given angle. 750o

A) $\frac { 25 \pi } { 3 }$
B) $\frac { 25 \pi } { 6 }$
C) $\frac { 75 \pi } { 2 }$
D) $\frac { 25 \pi } { 2 }$
E) $\frac { 25 \pi } { 12 }$

Question 13

A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure). For a circle of radius $r,$ the area $A$ of a sector of the circle with central angle $\theta$ (measured in radians) is given by $A = \frac { 1 } { 2 } r ^ { 2 } \theta$ . A sprinkler system on a farm is set to spray water over a distance of $60$ feet and rotates through an angle of $110 ^ { \circ }$ . Use the above given information to find the area of the region. Round your answer to two decimal places.

A)3457.14
B)314.29
C)3300.00
D)1728.57
E)12,100.00

Question 14

A compact disc can have an angular speed up to 3146 radians per minute. At this angular speed, how many revolutions per minute would the CD make? Round your answer to the nearest integer.

A)122
B)143
C)919
D)501
E)72

Question 15

Find $\csc \theta$ from the given graph.

A) $\frac { 15 } { 17 }$
B) $- \frac { 8 } { 17 }$
C) $- \frac { 17 } { 8 }$
D) $\frac { 17 } { 8 }$
E) $- \frac { 17 } { 15 }$

Question 16

Find the degree measure of the given angle. $\frac { 4 \pi } { 7 }$

A)280.0o
B)102.9o
C)157.5o
D)315.0o
E)32.7o

Question 17

Solve the triangle for the indicated angle.

A)angle $\theta :$ 40 $^\circ$
B)angle $\theta :$ 90 $^\circ$
C)angle $\theta :$ 140 $^\circ$
D)angle $\theta :$ 50 $^\circ$
E)angle $\theta :$ 130 $^\circ$

Question 18

Solve the triangle for the indicated side.

A) $\text { side } h : \frac { 7 } { 8 }$
B) $\text { side } h : \quad \frac { 15 } { 7 }$
C) $\text { side } h : \quad \frac { 8 } { 7 }$
D) $\text { side } h : \frac { 7 } { 15 }$
E) $\text { side } h : \frac { 4 } { 7 }$

Question 19

Find the cosine of $\theta$ .

A) $\frac { 4 } { 3 }$
B) $\frac { 4 } { 5 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 5 } { 4 }$
E) $\frac { 5 } { 3 }$

Question 20

Determine the quadrant in which $\theta$ lies if sin q < 0 and cos q > 0.

A)fourth quadrant
B)third quadrant
C)first quadrant
D)second quadrant
E)second or third quadrants

Question 21

Find the period of the trigonometric function. $y = \cot \frac { \pi x } { 6 }$

A) $\frac { \pi } { 6 }$
B) $6$
C) $\frac { \pi } { 3 }$
D) $\frac { \pi } { 2 }$
E) $\pi$

Question 22

Find two values of q that satisfy the equation below. Give values of q in radians $( 0 \leq \theta \leq 2 \pi )$ . Do not use a calculator. sin q = $\frac { \sqrt { 2 } } { 2 }$

A) $\theta = \frac { \pi } { 3 },$ $\theta = \frac { 3 \pi } { 4 }$
B) $\theta = \frac { \pi } { 4 }$ , $\theta = \frac { 3 \pi } { 4 }$
C) $\theta = \frac { \pi } { 4 },$ $\theta = \pi$
D) $\theta = \frac { \pi } { 6 },$ $\theta = \frac { 5 \pi } { 6 }$
E) $\theta = \frac { \pi } { 4 },$ $\theta = \frac { 4 \pi } { 3 }$

Question 23

Find the derivative of the trigonometric function. $y = \cos 3 x + \sin ^ { 2 } x$

A) $- 3 \sin 3 x + 2 \sin x \cos x$
B) $3 \sin 3 x - 2 \sin x \cos x$
C) $3 \sin 3 x + 2 \sin ^ { 2 } x \cos x$
D) $- \sin 3 x + 2 \sin ^ { 2 } x \cos ^ { 2 } x$
E) $- 3 \sin ^ { 2 } x + \sin ^ { 2 } x \cos ^ { 2 } x$

Question 24

Approximate using a calculator (set for radians). Round answers to two decimal places. $\sin 2$

A)1.00
B)0.91
C)0.08
D)-0.42
E)-1.00

Question 25

Solve the equation below for $\theta$ $( 0 \leq \theta \leq 2 \pi )$ . For some of the equations you should use the trigonometric identities listed in this section. Use the trace feature of a graphing utility to verify your results. $\sin 2 \theta - \cos \theta = 0$

A) $\frac { \pi } { 4 } , \frac { 5 \pi } { 4 }$
B) $\frac { \pi } { 4 } , \frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 4 }$
C) $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 3 \pi } { 6 }$
D) $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$
E) $\frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 }$

Question 26

Sketch the graph of the function $y = 3 \tan \pi x$ .

A)
B)
C)
D)
E)

Question 27

Solve the equation below for $\theta$ $( 0 \leq \theta \leq 2 \pi )$ . For some of the equations you should use the trigonometric identities listed in this section. Use the trace feature of a graphing utility to verify your results. $\cos ^ { 2 } \theta + \sin \theta = 1$

A) $0 , \pi , 2 \pi$
B) $0 , \frac { \pi } { 2 } , \pi , 2 \pi$
C) $\pi , \frac { 2 \pi } { 3 }$
D) $\frac { \pi } { 3 } , \frac { 5 \pi } { 3 }$
E) $0 , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \pi$

Question 28

Find the period and amplitude of the function $y = \frac { 7 } { 2 } \sin \left( \frac { \pi x } { 2 } \right)$ .

A)Period: $2 \pi$ ; Amplitude:7
B)Period: $2 \pi$ ; Amplitude: $\frac { 7 } { 2 }$
C)Period: $2$ ; Amplitude: $\frac { 7 } { 2 }$
D)Period: $4$ ; Amplitude: 7
E)Period: $4$ ; Amplitude: $\frac { 7 } { 2 }$

Question 29

Match the function below with the correct graph. $y = \sin x$

A)
B)
C)
D)
E)

Question 30

Find a and d for $f ( x ) = a \cos x + d$ such that the graph of f matches the figure.

A) $a = 2 ; d = 3$
B) $a = 5 ; d = 2$
C) $a = 3 ; d = 5$
D) $a = 3 ; d = 2$
E) $a = 5 ; d = 5$

Question 31

Find the period of the trigonometric function. $y = 3 \sec 5 x$

A) $\frac { \pi } { 5 }$
B) $\frac { 2 \pi } { 3 }$
C) $\frac { \pi } { 3 }$
D) $\frac { 2 \pi } { 5 }$
E) $\frac { 3 \pi } { 5 }$

Question 32

Sketch the graph of the function $y = 2 \sec 3 x$ .

A)
B)
C)
D)
E)

Question 33

Solve the equation for $\theta$ $( 0 \leq \theta \leq 2 \pi )$ . For some of the equations you should use the trigonometric identities listed in this section. Use the trace feature of a graphing utility to verify your results. $\cos 2 \theta + 3 \cos \theta + 2 = 0$

A) $\frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \pi$
B) $\frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , 2 \pi$
C) $0 , \frac { 2 \pi } { 3 } , \frac { 4 \pi } { 3 } , \pi$
D) $0 , \frac { \pi } { 3 } , \frac { 4 \pi } { 3 }$
E) $0 , \frac { \pi } { 3 } , \frac { 4 \pi } { 3 } , \pi$

Question 34

Use a calculator to evaluate the trigonometric function $\cos 400 ^ { \circ }$ to four decimal places.

A)-1.0827
B)1.1918
C)-0.9236
D)0.7660
E)0.8391

Question 35

Sketch the graph of the function $y = \csc 2 x$ .

A)
B)
C)
D)
E)

Question 36

Find two values of q that satisfy the equation below. Give values of q in radians $( 0 \leq \theta \leq 2 \pi )$ . Do not use a calculator. sin q = $- \frac { \sqrt { 3 } } { 2 }$

A) $\theta = \frac { \pi } { 3 },$ $\theta = \frac { 5 \pi } { 3 }$
B) $\theta = \frac { \pi } { 3 },$ $\theta = \pi$
C) $\theta = \frac { 4 \pi } { 3 }$ , $\theta = \frac { 5 \pi } { 3 }$
D) $\theta = \frac { \pi } { 6 },$ $\theta = \frac { 7 \pi } { 6 }$
E) $\theta = \frac { \pi } { 3 }$ , $\theta = \frac { 5 \pi } { 3 }$

Question 37

In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 4.5 $^\circ$ . After you drive 13 miles closer to the mountain, the angle of elevation is 11 $^\circ$ . Approximate the height of the mountain. Round your answer to two decimal places.

A)45.50 miles
B)8.84 miles
C)1.94 miles
D)1.72 miles
E)17.69 miles

Question 38

Evaluate without using a calculator, leaving the answers in exact form. $\cos \frac { 2 \pi } { 3 }$

A) $\frac { \sqrt { 3 } } { 2 }$
B) $\frac { \sqrt { 2 } } { 2 }$
C)1
D) $\frac { 1 } { 2 }$
E) $- \frac { 1 } { 2 }$

Question 39

Find the period and amplitude of the function $y = 3 \cos 2 x$ .

A)period: $2 \pi$ ; amplitude: 6
B)period: $2 \pi$ ; amplitude: 3
C)period: $\pi$ ; amplitude: 3
D)period: $\pi$ ; amplitude: 6
E)period: $\frac { \pi } { 2 }$ ; amplitude: 3

Question 40

A 20-foot ladder leaning against the side of a house makes a 75 $^\circ$ angle with the ground (see figure). How far up the side of the house does the ladder reach? Round your answer to four decimal places.

A)19.3185 feet
B)20.7055 feet
C)5.1764 feet
D)5.3590 feet
E)77.2741 feet

Question 41

Find the derivative of the function. $f ( \theta ) = \frac { 3 } { 7 } \sin ^ { 2 } 3 \theta$

A) $f ^ { \prime } ( \theta ) = \frac { 3 \sin 3 \theta \cos 3 \theta } { 7 }$
B) $f ^ { \prime } ( \theta ) = \frac { 18 \sin 3 \theta \cos 3 \theta } { 7 }$
C) $f ^ { \prime } ( \theta ) = \frac { 18 \cos 3 \theta } { 7 }$
D) $f ^ { \prime } ( \theta ) = - \frac { 18 \sin 3 \theta \cos 3 \theta } { 7 }$
E) $f ^ { \prime } ( \theta ) = \frac { 18 \sin 3 \theta } { 7 }$

Question 42

Find the derivative of the function. $y = 2 \cos 5 x$

A) $y ^ { \prime } = - 10 \sin 5 x$
B) $y ^ { \prime } = 10 \sin 5 x$
C) $y ^ { \prime } = - 2 \sin 5 x$
D) $y ^ { \prime } = - 10 \cos 5 x$
E) $y ^ { \prime } = - 5 \sin 5 x$

Question 43

Find the indefinite integral of $\int e ^ { x } \sin e ^ { x } d x$ .

A) $e ^ { x } \cos e ^ { x } + C$
B) $e ^ { x } - \sin e ^ { x } + C$
C) $- \cos e ^ { x } + C$
D) $\cos e ^ { x } + C$
E) $\sin e ^ { x } + C$

Question 44

The normal average daily temperature in degrees Fahrenheit for a city is given by $51 - 23 \cos \frac { 5 \pi ( t - 33 ) } { 365 }$ where t is the time in days, with $t = 1$ corresponding to January 1. Find the warmest day.

A)March 17
B)March 16
C)April 17
D)April 16
E)April 15

Question 45

Evaluate the definite integral $\int _ { \frac { \pi } { 36 } } ^ { \frac { \pi } { 22 } } \csc 6 x \cot 6 x d x$ .

A)6
B)-6
C) $- \frac { 1 } { 6 }$
D) $\frac { 1 } { 6 }$
E) $\infty$

Question 46

The average monthly precipitation P (in inches), including rain, snow, and ice, for Sacramento, California can be modeled by $P = 2.47 \sin ( 0.40 t + 1.80 ) + 2.08,$ $0 \leq t \leq 12$ where $t$ is the time (in months), with $t = 1$ corresponding to January. Find the total annual precipitation for Sacramento.

A) $18.02$ in.
B) $17.69$ in.
C) $14.52$ in.
D) $16.57$ in.
E) $18.90$ in.

Question 47

Suppose that the numbers W (in thousands) of construction workers employed in the United States during 2006 can be modeled by $W = 9094 + 455.2 \sin ( 0.6 t - 1.813 )$ where t is the time in months, with $t = 1$ corresponding to January 1. Approximate the month t in which the number of construction workers employed was a maximum. What was the maximum number of construction workers employed? Round your answer to nearest hundredth.

A)July; The maximum number of construction workers employed is 9559.
B)May; The maximum number of construction workers employed is 9539.
C)June; The maximum number of construction workers employed is 9539.
D)May; The maximum number of construction workers employed is 9549.
E)June; The maximum number of construction workers employed is 9549.

Question 48

Determine the relative extrema of the function $y = 2 \cos x + \sin 2 x$ on the interval $( 0,2 \pi )$ .

A)relative minimum: $\left( \frac { 5 \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { 5 \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$
B)relative minimum: $\left( \frac { 5 \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$
C)relative minimum: $\left( \frac { \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { 5 \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$
D)relative minimum: $\left( \frac { \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { 5 \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$
E)relative minimum: $\left( \frac { 5 \pi } { 6 } , \frac { 3 \sqrt { 3 } } { 2 } \right)$ relative maximum: $\left( \frac { \pi } { 6 } , - \frac { 3 \sqrt { 3 } } { 2 } \right)$

Question 49

Evaluate the definite integral. $\int _ { 0 } ^ { \pi / 4 } 4 \sec ^ { 2 } 3 t c t$

A) $- 4$
B) $7$
C)0
D)undefined
E)4

Question 50

Find the indefinite integral. $\int \tan ^ { 3 } x \sec ^ { 2 } x d x$

A) $- \frac { 1 } { 6 } \tan ^ { 3 } x \sec ^ { 2 } x + C$
B) $\frac { 1 } { 12 } \tan ^ { 4 } x \sec ^ { 3 } x + C$
C) $\frac { 1 } { 4 } \tan ^ { 4 } x + C$
D) $\frac { 1 } { 4 } \tan ^ { 4 } x \sec ^ { 4 } x + C$
E) $\frac { 1 } { 4 } \sec ^ { 4 } x + C$

Question 51

Find the indefinite integral of the following function. $\int \cos 2 t d t$

A) $\cos 2 t + C$
B) $\sin 2 t + C$
C) $2 \sin 2 t$
D) $\frac { \sin 2 t } { 2 } + C$
E) $\frac { \sin 2 t } { 3 }$

Question 52

For a person at rest, the velocity v (in liters per second) of air flow into and out of the lungs during a respiratory cycle is given by $0.9 \sin \frac { \pi t } { 7 }$ , where t is the time in seconds. Inhalation occurs when $v > 0$ and exhalation occurs when $v < 0$ . Find the time for one full respiratory cycle.

A) $14 \pi$ seconds
B) $\pi$ seconds
C)14 seconds
D) $2 \pi$ seconds
E)7 seconds

Question 53

Find the derivative of the function $y = \ln \left( \cos ^ { 2 } x \right)$ and simplify your answer by using the trigonometric identities.

A) $y = 2 \tan x$
B) $y = \frac { 2 } { \cos x \sin x }$
C) $y = - 2 \tan x$
D) $y = 2 \cot x$
E) $y = - 2 \cot x$

Question 54

Find the indefinite integral of $\int \frac { \sec x \tan x } { \sec x - 2 } d x$ .

A) $\ln | \sec x + 2 | + C$
B) $\ln | \sec x - 2 | + C$
C) $\ln | 2 \cos x + \sec x | + C$
D) $\ln | \cos x - 2 | + C$
E) $\ln | \cos x + 2 | + C$

Question 55

Find the indefinite integral of the following function. $\int 4 x ^ { 3 } \cos x ^ { 4 } d x$

A) $\cos x ^ { 4 } + C$
B) $\sin x ^ { 4 } + C$
C) $\sin x ^ { 3 }$
D) $\frac { \sin x ^ { 4 } } { 4 } + C$
E) $\sin x ^ { 4 }$

Question 56

Find the indefinite integral. $\int \sec ^ { 6 } \frac { x } { 4 } \tan \frac { x } { 4 } d x$

A) $\frac { 2 } { 3 } \sec ^ { 6 } \frac { x } { 4 } \tan \frac { x } { 4 } + C$
B) $\frac { 2 } { 3 } \sec ^ { 6 } \frac { x } { 4 } + C$
C) $\frac { 1 } { 6 } \sec ^ { 7 } \frac { x } { 4 } + C$
D) $\frac { 1 } { 4 } \sec ^ { 6 } \frac { x } { 4 } \tan \frac { x } { 4 } + C$
E) $\frac { 1 } { 3 } \tan \frac { x } { 4 } + C$

Question 57

Find an equation of the tangent line to the graph of the function at the given point. $y = \cot x$ $\left( \frac { 3 \pi } { 4 } , - 1 \right)$

A) $y = - 2 x + \frac { 3 } { 2 } \pi - 1$
B) $y = 2 x + \frac { 1 } { 2 } \pi - 1$
C) $y = - 2 x - \frac { 1 } { 2 } \pi$
D) $y = - x - \frac { 5 } { 2 } \pi - 1$
E) $y = 2 x - \frac { 3 } { 2 } \pi + 1$

Question 58

Determine the relative extrema of the function $e ^ { 5 x } \cos x$ on the interval $( 0,2 \pi )$ .

A)relative minimum: $\left( - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } , \frac { 5 \pi } { 4 } \right)$ relative maximum: $\left( \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } , \frac { \pi } { 4 } \right)$
B)relative minimum: $\left( \frac { \pi } { 4 } , - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } \right)$ relative maximum: $\left( \frac { 5 \pi } { 4 } , \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } \right)$
C)relative minimum: $\left( \frac { 5 \pi } { 4 } , - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } \right)$ relative maximum: $\left( \frac { \pi } { 4 } , \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } \right)$
D)relative minimum: $\left( \frac { 5 \pi } { 4 } , \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } \right)$ relative maximum: $\left( \frac { \pi } { 4 } , - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } \right)$
E)relative minimum: $\left( \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 5 \pi } { 4 } } , \frac { 5 \pi } { 4 } \right)$ relative maximum: $\left( - \frac { \sqrt { 2 } } { 2 } e ^ { \frac { 25 \pi } { 4 } } , \frac { \pi } { 4 } \right)$

Question 59

Find the derivative of the function and simplify your answer by using the trigonometric identities $y = \cos ^ { 2 } x$

A) $- 2 \cos ^ { 2 } x \sin ^ { 2 } x = 2 \sin 2 x$
B) $2 \cos x \sin x = \sin 2 x$
C) $- 2 \cos x \sin x = - \sin 2 x$
D) $2 \cos ^ { 2 } x \sin x = 2 \sin x$
E) $2 \cos ^ { 2 } x \sin ^ { 2 } x = 2 \sin 2 x$

Question 60

Use integration by parts to find the indefinite integral. $\int x \cos 2 x d x$

A) $\frac { 1 } { 2 } x \cos 2 x - \frac { 1 } { 4 } \sin 2 x + C$
B) $\frac { 1 } { 2 } x \sin 2 x - \frac { 1 } { 4 } \cos 2 x + C$
C) $\frac { 1 } { 2 } \sin 2 x + \frac { 1 } { 2 } \cos 2 x + C$
D) $\frac { 1 } { 2 } x \sin 2 x + \frac { 1 } { 4 } \cos 2 x + C$
E) $\frac { 1 } { 4 } x \cos 2 x + \frac { 1 } { 2 } \sin 2 x + C$