Deck 8: Trigonometric Functions

Question 1

The complex number is a root of the quadratic equation . Note: the quadratic equation has real coefficients.

Answer 1

a) -10
b)50

Question 2

Answer 2

a)4.62
b)1.91

Question 3

Answer 3

a)2
b)0

Question 4

In polar form, the complex number -6i is written , where r = _____ and = _____. Round the second answer to 2 decimal places, and give so that
.

Question 5

In polar form, the complex number is written , where r = _____ and = _____. Round both answers to 2 decimal places, and give so that .

Question 6

Question 7

Use deMoivre's formula to evaluate . Choose the root that lies in the first quadrant.

Question 8

Compute . Choose the root that lies in the first quadrant. Give your answer in Cartesian form, and round to 3 decimal places.

Question 9

Express in polar form.

Question 10

Find the square root of and give your answer in Cartesian form. Choose the root that lies in the fourth quadrant. Round your answer to 3 decimal places.

Question 11

Find the square root of and give your answer in Cartesian form. Choose the root that lies in the second quadrant. Round your answer to 3 decimal places.

Question 12

Compute and give your answer in Cartesian form. Choose the root that lies in the first quadrant. Round your answer to 3 decimal places.

Question 13

Find the Cartesian form for all 3 cube roots of . Round your answers to 3 decimal places.

Question 14

The roots of are complex numbers. Find the roots.

Question 15

The roots of are complex numbers. Find the roots.

Question 16

Write in Cartesian form.

Question 17

Express in polar form.

Question 18

Express in polar form.

Question 19

Express in polar form.

Question 20

Use de Moivre's formula to evaluate . Round your answer to 3 decimal places.

Question 21

What is the Cartesian equation for the circle shown below?

A)
B)
C)
D)

Question 22

Do all of the points satisfying , for , lie on the circle shown below?

Question 23

The origin is at the center of a clock, with the positive x-axis going through 3 and the positive y-axis going through 12. The hour hand is 9 cm long and the minute hand is 11 cm long. The Cartesian coordinates of the minute hand at 11:00 pm are ( _____, _____ ). Round both answers to 2 decimal places.

Question 24

The origin is at the center of a clock, with the positive x-axis going through 3 and the positive y-axis going through 12. The hour hand is 9 cm long and the minute hand is 11 cm long. The polar coordinates of the hour hand at 11:15 am are ( _____, _____ ). Round both answers to 2 decimal places.

Question 25

The inequalities and describe the region below. Round the last 2 answers to 3 decimal places, and be sure both are between 0 and .

Question 26

The cube root of 4-i which is in the second quadrant is equal to _____ + _____ i. Round both answers to 3 decimal places.

Question 27

Simplify
.

Question 28

Convert the polar equation to a Cartesian equation.

A)
B)
C)
D)

Question 29

Convert the equation to a polar equation.

A)
B)
C)
D)

Question 30

What are the polar inequalities that describe the cross section of a doughnut centered at the origin with a 5 inch diameter and a 1 inch hole?

A)
B)
C)
D)

Question 31

Describe the graph of the polar equation
.

A) A 4-petaled rose, each petal of length 3.
B) A 2-petaled rose, each petal of length 3.
C) A 3-petaled rose, each petal of length 2.
D) A 2-petaled rose, each petal of length 2.
E)
None of the above

Question 32

Which of the following are equations for the circle shown below? (The first two are Cartesian equations; the second two are polar equations)

A)
B)
C)
D)

Question 33

In which quadrant is a point with the polar coordinate -7 ?

Question 34

In which quadrant is a point with the polar coordinate -1.9 ?

Question 35

The polar coordinates of the Cartesian point (4, -5) are r = ______, = ______. Round both answers to 2 decimal points, and give so that .

Question 36

The Cartesian coordinates of the polar point (1.5, -2.25 ) are x = ______ and y = ______. Round both answers to 2 decimal places.

Question 37

Convert to rectangular coordinates. Classify the graph if possible.

Question 38

Write the polar equation of a circle of radius 4 centered at the origin.

Question 39

What is the equation in polar coordinates of a vertical line through the point

.

Question 40

Use inequalities to describe a ring centered at the origin whose outer radius is 2 and inner radius is 9 in polar coordinates.

Question 41

At which of the following values of x do the graphs of And intersect?

A)
B)
C)
D) None of the above

Question 42

Use the inverse sine function to estimate the solution to the equation for . Round to 2 decimal places.

Question 43

Find a solution in the interval for . Round to 3 decimal places.

Question 44

Use a graph of to estimate the solution to the equation for . Round to 2 decimal places.

Question 45

Which of the following are x-intercepts of the function ?

A) 0
B)
C)
D)
E)
F)
G) None of the above

Question 46

Find all solutions to on the interval . Give your answers correct to 3 decimal places.

Question 47

Find all solutions to the equation for Give your answers to 3 decimal places.

Question 48

The baseball field's usage (in people per week) is seasonal with the peak in mid-July and the low in mid-January. The usage is 1500 in July and 500 in January. Find a trig function representing the usage at time t months after mid-January.

Question 49

Which of the following are defined?

A)
B)
C)
D)
E)
F)

Question 50

Find all values of such that and . Give answers correct to 3 decimal places.

Question 51

Find all solutions (if possible) with t in radians: . Give answers correct to 3 decimal places.

Question 52

Find all solutions (if possible) with t in radians: . Give answers correct to 3 decimal places.

Question 53

Find all solutions to for Give answers correct to 3 decimal places.

Question 54

Find all solutions to for Give answers correct to 3 decimal places.

Question 55

How many solutions to are there for

Question 56

How many solutions to are there for

Question 57

How many solutions to are there for

Question 58

Solve for

Question 59

Solve for

Question 60

Solve for

Question 61

What is the amplitude of ?

Question 62

Consider the function . What happens to the graph of as ?

A)
B)
C)
D)
E)

Question 63

Constructive and destructive interference are defined in the following figure from an engineering textbook. Let ,
,
, and . Do f(x) and h(x) have constructive interference, destructive interference, or neither?

Question 64

Question 65

Use a calculator to graph the function on the interval .

has a minimum value of _____ at x = _____. Round both answers to 2 decimal places.

Question 66

Without a calculator, find the exact value of . If it is undefined, enter "undefined".

Question 67

Which of the following quotients is equivalent to ?

A)
B)
C)

Question 68

Without a calculator, find the exact value of . If it is undefined, enter "undefined".

Question 69

Without a calculator, find the exact value of . If it is undefined, enter "undefined".

Question 70

a)
b)

Question 71

If find an expression for in terms of y.

Question 72

Simplify .

Question 73

Question 74

Simplify .

Question 75

Using the identity find an angle such that .

Question 76

Let P be a point on the unit circle with coordinates corresponding to an angle of t radians. Write
in terms of x and y.

Question 77

Let P be a point on the unit circle with coordinates corresponding to an angle of t radians. Write in terms of x and y.

Question 78

Let P be a point on the unit circle with coordinates corresponding to an angle of t radians. Write in terms of x and y.

Question 79

Simplify (For values for which it is defined).

A)
B)
C)
D)

Question 80

Simplify (for values of the variable for which it is defined).

A)
B)
C)
D) None of the above.
1)5