Deck 4: Trigonometric Functions

Question 1

Find the amplitude of the graph of

Answer 1

2

Question 2

Let sin
Find tan x

Answer 2

Question 3

From a 75 -foot observation tower, a controller sights a hot-air balloon at an angle of elevation. If the horizontal distance from the tower to the balloon is 300 feet, how much higher in the air is the balloon?

Answer 3

109.19 FEET

Question 4

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Question 5

The lengths of the hypotenuse and one leg of a right triangle are 10.5 and 3.7, respectively. Find the measure of the angle opposite the leg whose length is known.

A)
B)
C)
D)
E)

Question 6

Find the period of y=3 tan (2x-1) .

Question 7

State the domain, range, and period of the function

Question 8

Question 9

Jeana sights the top of a building and finds the angle of elevation to be She moves 100 feet closer and finds that the angle is now What is the height of the building?

Question 10

If sin t=0.5299 and cos t=0.8481 , then tan t=

Question 11

What is the period of y=sin 6 x ?

Question 12

The wheel of a train engine turns as it moves a distance of 4.75 yards. What is the diameter of the wheel of the engine?

Question 13

Find the range of the graph of

A)
B)
C)
D)
E)

Question 14

Find an algebraic expression equivalent to

A)
B)
C)
D)
E)

Question 15

A guy wire is stretched from the top of a 200 ft transmission tower to a point on the ground 130ft from the center of the base of the tower. What angle, in degrees, does the guy wire make with the ground?

Question 16

Sketch the graph of y= 3sec x for

Question 17

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Question 18

Sketch one period of the graph of y= sin2x + sin3x.

Question 19

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FORM A DATE
4 Chapter Test NAME
Directions: Show all work where appropriate. A graphing calculator may be necessary to answer
some questions.

Question 20

Find the domain of

A)
B)
C)
D)
E)

Question 21

Question 22

Question 23

For the next 10 years, a small company's business volume can be modeled by the function
where x is the number of years after 2006 and f is the sales in millions of dollars.
(a) What are the company's sales in 2006?
(b) What does the model predict for sales in 2012?
(c) How many years are in each economic cycle for this company?

Question 24

Solve the right triangle for all its unknown parts if and b=4.5

Question 25

Which transformation was not performed on y=cos x to obtain

A) Vertical stretch by a factor of 4
B) Reflection through the x -axis
C) Horizontal stretch by a factor of 2
D) Horizontal shrink by a factor of
E) Horizontal shift left units

Question 26

Find approximate values of a, b , and h (to the nearest hundredth) so that f(x)=2 sin 5x-4 cos 5x

Question 27

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FORM A
4 Chapter Test (continued) NAME

Question 28

Solve the equation \cot x=2.7 for x in the interval graphically. Estimate answers to the nearest hundredth.

Question 29

Find an equivalent algebraic expression not involving trig functions for cos
Explain why your expression includes (or does not include) a sign.

Question 30

The wheels on a truck are turning at 550 revolutions per
minute as the truck travels at 55 miles per hour. What is
the radius, in inches, of the wheels on the truck?

Question 31

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Question 32

Compute sec 2 .

Question 33

In the space below, explain how the graph of the
function is related to a basic trigonometric
graph. Determine the period, domain, range, zeros, and asymptotes (if any). Then sketch the graph of the function.

Question 34

State the amplitude, period, phase shift, and vertical translation of the sinusoid.

Question 35

Which transformation was not performed on y=\sin x to obtain

A)
B) Horizontal stretch by a factor of 3
C) Vertical stretch by a factor of 2
D) Reflection through the x -axis
E)

Question 36

The wheels on a truck are turning at 630 revolutions per minute as the truck travels at 60 miles per hour. What is the radius, in inches, of the wheels on the truck?

Question 37

Question 38

Which is the correct value of
(Express the answer in radians to the nearest hundredth.)

A) 1.77
B) 0.64
C) 95.49
D) 36.87
E) 0.03

Question 39

Evaluate all six trigonometric functions of the angle

Question 40

the tall building?

Question 41

Question 42

Which is the correct value of (Express the answer in radians to the nearest hundredth.)

A) 1.00
B) 1.09
C) 1.53
D) 87.71
E) 1.16

Question 43

Question 44

Solve the equation cot x=-3.2 for x in the interval graphically. Estimate answers to the nearest hundredth.

Question 45

Question 46

For the next ten years, a small company's business volume can be modeled by the function

where x is the number
of years after 2006 and f is the sales in millions of dollars.
(a) What are the company's sales in 2006?
(b) What does the model predict for sales is 2015 ?
(c) How many years are in each economic cycle for this company?

Question 47

Find an equivalent algebraic expression not involving trig functions for csc
Explain why your expression includes (or does not include) a sign.

Question 48

In the space below, explain how the graph of the function y=-sec 2 x is related to a basic trigonometric graph. Determine the period, domain, range, zeros, and asymptotes (if any). Then sketch the graph of the function.

Question 49

The angle of elevation from the top of a building to the top of a nearby taller building is and the angle of depression to the bottom of the taller building is If the short building is 61.7m high, what is the height of the tall building?

Question 50

For each of the following functions, determine if the graph shows damped oscillation. If so, state the damping factor.
(a)
(b)
(c)
(d)
(e)