Chapter 5

Question 1

tanθ

Answer 1

sinθ/cosθ

Question 2

cotθ

Answer 2

cosθ/sinθ

Question 3

sinθ

Answer 3

1/cscθ

Question 4

cosθ

Answer 4

1/secθ

Question 5

tanθ

Answer 5

1/cotθ

Question 6

cscθ

Answer 6

1/sinθ

Question 7

secθ

Answer 7

1/cosθ

Question 8

cotθ

Answer 8

1/tanθ

Question 9

1

Answer 9

sin²θ + cos²θ

sec²θ - tan²θ

csc²θ - cot²θ

Question 10

sin[(π/2) - θ]

Answer 10

cosθ

Question 11

cos[(π/2) - θ]

Answer 11

sinθ

Question 12

tan[(π/2) - θ]

Answer 12

cotθ

Question 13

csc[(π/2) - θ]

Answer 13

secθ

Question 14

sec[(π/2) - θ]

Answer 14

cscθ

Question 15

cot[(π/2) - θ]

Answer 15

tanθ

Question 16

sin(-θ)

Answer 16

-sinθ

Question 17

cos(-θ)

Answer 17

cosθ

Question 18

tan(-θ)

Answer 18

-tanθ

Question 19

csc(-θ)

Answer 19

-cscθ

Question 20

sec(-θ)

Answer 20

secθ

Question 21

cot(-θ)

Answer 21

-cotθ

Question 22

Verifying trigonometric identities

Answer 22

1. work with one side at a time
2. factor, add fractions, square a binomial
3. fundamental identities
4. convert all to sin cos
5. try something

Question 23

sin(x+-y)

Answer 23

sinxcosy +- sinycosx

Question 24

cos(x+-y)

Answer 24

cosxcosy -+ sinxsiny

Question 25

tan(x+-y)

Answer 25

tanx+-tany / 1 -+ tanxtany

Question 26

2x

Answer 26

(x + x)

Question 27

sin2x

Answer 27

2sinxcosx

Question 28

cos2x

Answer 28

cos²x - sin²x 2cos² - 1 1 - 2sin²x

Question 29

tan2x

Answer 29

2tanx / 1 - tan²x

Question 30

sin²x

Answer 30

1-cos2x/2

Question 31

cos²x

Answer 31

1+cos2x/2

Question 32

tan²x

Answer 32

1-cos2x/1+cos2x

Question 33

sinx/2

Answer 33

+-√1-cosx/2 sign depends on the quadrant u/2 lies in

Question 34

cosx/2

Answer 34

+-√1+cosx/2 sign depends on the quadrant u/2 lies in

Question 35

tanx/2

Answer 35

1-cosx/sinx = sinx/1+cosx

Question 36

Quadratic formula

Answer 36

-b±√b²-4ac/2a