Deck 7: Analytic Trigonometry

Question 1

Verify the identity.

Answer 1

Question 2

Verify the identity.

Answer 2

Question 3

Simplify.

Answer 3

Question 4

Simplify.

Question 5

Verify the identity.

Question 6

Verify the identity.

Question 7

Simplify.

Question 8

Simplify the trigonometric expression.

Question 9

Verify the identity.

Question 10

Write in terms of and then simplify.

Question 11

Simplify.

Question 12

Verify the identity.

Question 13

Verify the identity.

Question 14

Simplify.

Question 15

Simplify.

Question 16

Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that

Question 17

Simplify the trigonometric expression.

Question 18

Write in terms of and then simplify.

Question 19

Verify the identity.

Question 20

Write in terms of and then simplify.

Question 21

Use addition or subtraction formulas to find the exact value of .

Question 22

Use addition or subtraction formulas to find the exact value of .

Question 23

Prove .

Question 24

Use an addition or subtraction formula to write and find its exact value.

Question 25

Use an addition or subtraction formula to write and find its exact value.

Question 26

Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that

Question 27

Use an addition or subtraction formula to write and find its exact value.

Question 28

Show that the equation is not an identity.

Question 29

Prove .

Question 30

Use addition or subtraction formulas to find the exact value of .

Question 31

Use an addition or subtraction formula to write and find its exact value.

Question 32

Use addition or subtraction formulas to find the exact value of .

Question 33

Prove .

Question 34

Prove .

Question 35

Use an addition or subtraction formula to write and find its exact value.

Question 36

Prove .

Question 37

Use addition or subtraction formulas to find the exact value of .

Question 38

Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that

Question 39

Use an addition or subtraction formula to write and find the exact value.

Question 40

Make the indicated trigonometric substitution in the given algebraic expression and simplify. Assume that

Question 41

Find , and , given that and .

Question 42

Use a half-angle formula to find the exact value of .

Question 43

Use a half-angle formula to find the exact value of .

Question 44

Find , and , given that and is in quadrant II.

Question 45

Use a double-angle formula or a half-angle formula to simplify .

Question 46

Find , and , given that and .

Question 47

Find , and , given that and .

Question 48

Prove .

Question 49

Find the exact value of the expression.

Question 50

Find the exact value of the expression.

Question 51

Prove .

Question 52

Find , and , given that and is in quadrant IV.

Question 53

Find the exact value of the expression.

Question 54

Use a half-angle formula to find the exact value of .

Question 55

Use a half-angle formula to find the exact value of .

Question 56

Use the formula to find the acute angle formed by the two lines and .

Question 57

Write the given expression in terms of x and y only.

Question 58

Write in terms of sine only.

Question 59

Use a half-angle formula to find the exact value of .

Question 60

Write the given expression in terms of x and y only.

Question 61

Use a double-angle formula or half-angle formula to simplify .

Question 62

Write as a sum.

Question 63

Find the exact value.

Question 64

Find the exact value.

Question 65

Write the product as a sum.

Question 66

Use a double-angle formula or a half-angle formula to simplify .

Question 67

Write the sum as a product.

Question 68

Solve the given equation.

Question 69

Write the sum as a product.

Question 70

Use a double-angle formula or a half-angle formula to simplify .

Question 71

Prove .

Question 72

Solve the given equation.

Question 73

Use a double-angle formula or half-angle formula to simplify .

Question 74

Prove .

Question 75

Solve the given equation.

Question 76

Write the sum as a product.

Question 77

Write the product as a sum.

Question 78

Use a double-angle formula or a half-angle formula to simplify .

Question 79

Use a double-angle formula or a half-angle formula to simplify .

Question 80

Write as a product.