Deck 5: Trigonometric Identities

Question 1

Solve the equation for exact solutions.

Answer 1

Question 2

Verify that the equation is an identity.
sin(x + y)- sin(x - y)= 2 cos x sin y

Answer 2

sin (x + y)- sin (x - y)= sin x cos y + cos x sin y - sin x cos y + cos x sin y = 2 cos x
sin y.

Question 3

Solve the equation for exact solutions.

Answer 3

Question 4

Verify that each equation is an identity.

Question 5

Verify that each equation is an identity.

Question 6

Verify that the equation is an identity.
cos(x - y)- cos(x + y)= 2 sin x sin y

Question 7

Verify that the equation is an identity.

Question 8

Verify that the equation is an identity.

Question 9

Verify that the equation is an identity.

Question 10

Verify that the equation is an identity.

Question 11

Verify that the equation is an identity.

Question 12

Solve the equation for exact solutions.

Question 13

Verify that each equation is an identity.

Question 14

Solve the equation for exact solutions.

Question 15

Verify that the equation is an identity.

Question 16

Verify that each equation is an identity.

Question 17

Verify that each equation is an identity.

Question 18

Verify that each equation is an identity.

Question 19

Verify that each equation is an identity.

Question 20

Verify that each equation is an identity.

Question 21

Verify that each equation is an identity.

Question 22

Verify that each equation is an identity.

Question 23

Provide an appropriate response.
Graph the expression cos x + sin x tan x on your calculator. Determine what constant or
single circular function is equivalent to the given expression.

Question 24

Verify that each equation is an identity.

Question 25

Verify that the equation is an identity.

Question 26

Verify that each equation is an identity.

Question 27

Verify that each equation is an identity.

Question 28

Verify that each equation is an identity.

Question 29

Verify that each equation is an identity.

Question 30

Provide an appropriate response.

Question 31

Provide an appropriate response.

Question 32

Verify that the equation is an identity.

Question 33

Verify that each equation is an identity.

Question 34

Verify that the equation is an identity.

Question 35

Verify that the equation is an identity.

Question 36

Verify that each equation is an identity.

Question 37

Verify that the equation is an identity.

Question 38

Verify that each equation is an identity.

Question 39

Verify that each equation is an identity.

Question 40

Verify that each equation is an identity.

Question 41

Perform the indicated operations and simplify the result so there are no quotients.

Question 42

Verify that each equation is an identity.

Question 43

Use a sum or difference identity to find the exact value.

Question 44

Verify that each equation is an identity.
tan x(csc x - sin x)= cos x

Question 45

Use the cofunction identities to find an angle that makes the statement true.
tan (2ϴ - 140°)= cot (ϴ + 5°)

A)ϴ = 6°
B)ϴ = 75°
C)ϴ = 10°
D)ϴ = 16°

Question 46

Verify that each equation is an identity.

Question 47

Verify that the equation is an identity.

Question 48

Verify that each equation is an identity.

Question 49

Use a sum or difference identity to find the exact value.

Question 50

Verify that the equation is an identity.

Question 51

Verify that the equation is an identity.

Question 52

Verify that the equation is an identity.

Question 53

Verify that the equation is an identity.

Question 54

Verify that each equation is an identity.

Question 55

Write in terms of the cofunction of a complementary angle.

Question 56

Use a graphing calculator to make a conjecture as to whether each equation is an identity.
cos(x + y)= cos x + cos y

A)Identity
B)Not an Identity

Question 57

Verify that the equation is an identity.

Question 58

Use the fundamental identities to simplify the expression.

Question 59

Verify that the equation is an identity.

Question 60

Use identities to write each expression as a function of .

Question 61

Solve the problem.

Question 62

Graph the expression on each side of the equals symbol to determine whether the equation might be an identity.

Question 63

Solve the problem.
When a person bends at the waist with a straight back, the force, F, exerted by the person's lower back muscles can be estimated with the formula F = 2.89w sin (ϴ + 90°), where w is the person's
Weight, and ϴ is the angle made by the person's torso relative to the horizontal. Suppose that a
120-pound person bends at an angle of 30°. Determine the force exerted by the person's back
Muscles, and estimate the angle that requires the back muscles to exert a force of 208 pounds.
Round the force to the nearest pound, and the angle to the nearest tenth, if necessary.

A)300 pounds; 30°
B)300 pounds; 53.1°
C)26 pounds; 53.1°
D)173 pounds; 47.3°

Question 64

Use the fundamental identities to find the value of the trigonometric function.

Question 65

Use identities to find the indicated value for each angle measure.

Question 66

Factor the trigonometric expression and simplify.

Question 67

Solve the problem.

Question 68

Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.

Question 69

Using a sum or difference identity, write the following as an expression involving functions of x.

Question 70

Factor the trigonometric expression and simplify.

Question 71

Using a sum or difference identity, write the following as an expression involving functions of x.

Question 72

Use a sum or difference identity to find the exact value.

Question 73

Using a sum or difference identity, write the following as an expression involving functions of x.

Question 74

Solve the problem.

Question 75

Find the exact value by using a half-angle identity.
cos 22.5°

Question 76

Use the fundamental identities to simplify the expression.

Question 77

Use the fundamental identities to simplify the expression.

Question 78

Solve the problem.

Question 79

Using a sum or difference identity, write the following as an expression involving functions of x.

Question 80

Use a sum or difference identity to find the exact value.