Trig Identities

Question 1

What is the reciprocal of sin(θ)?

Answer 1

csc(θ) = 1/sin(θ)

Question 2

What is the reciprocal of cos(θ)?

Answer 2

sec(θ) = 1/cos(θ)

Question 3

What is the reciprocal of tan(θ)?

Answer 3

cot(θ) = 1/tan(θ)

Question 4

What is tan(θ) in terms of sin and cos?

Answer 4

tan(θ) = sin(θ)/cos(θ)

Question 5

What is cot(θ) in terms of sin and cos?

Answer 5

cot(θ) = cos(θ)/sin(θ)

Question 6

What is the fundamental Pythagorean identity?

Answer 6

sin²(θ) + cos²(θ) = 1

Question 7

How is sec²(θ) related to tan²(θ)?

Answer 7

1 + tan²(θ) = sec²(θ)

Question 8

How is csc²(θ) related to cot²(θ)?

Answer 8

1 + cot²(θ) = csc²(θ)

Question 9

What is sin(90° - θ)?

Answer 9

cos(θ)

Question 10

What is cos(90° - θ)?

Answer 10

sin(θ)

Question 11

What is tan(90° - θ)?

Answer 11

cot(θ)

Question 12

Is sin(-θ) equal to sin(θ) or -sin(θ)?

Answer 12

-sin(θ)

Question 13

Is cos(-θ) equal to cos(θ) or -cos(θ)?

Answer 13

cos(θ)

Question 14

Is tan(-θ) equal to tan(θ) or -tan(θ)?

Answer 14

-tan(θ)

Question 15

What is sin(A + B)?

Answer 15

sin(A)cos(B) + cos(A)sin(B)

Question 16

What is cos(A + B)?

Answer 16

cos(A)cos(B) - sin(A)sin(B)

Question 17

What is tan(A + B)?

Answer 17

(tan(A) + tan(B)) / (1 - tan(A)tan(B))

Question 18

What is sin(2θ)?

Answer 18

2sin(θ)cos(θ)

Question 19

What is cos(2θ)?

Answer 19

cos²(θ) - sin²(θ)

Question 20

What is tan(2θ)?

Answer 20

2tan(θ) / (1 - tan²(θ))

Question 21

What is sin(θ/2)?

Answer 21

±√((1 - cos(θ))/2)

Question 22

What is cos(θ/2)?

Answer 22

±√((1 + cos(θ))/2)

Question 23

What is tan(θ/2)?

Answer 23

±√((1 - cos(θ)) / (1 + cos(θ)))

Question 24

What is sin(A)sin(B) in sum form?

Answer 24

1/2 [cos(A - B) - cos(A + B)]

Question 25

What is cos(A)cos(B) in sum form?

Answer 25

1/2 [cos(A - B) + cos(A + B)]

Question 26

What is sin(A)cos(B) in sum form?

Answer 26

1/2 [sin(A + B) + sin(A - B)]

Question 27

What is sin(A) + sin(B) in product form?

Answer 27

2sin((A + B)/2)cos((A - B)/2)

Question 28

What is cos(A) + cos(B) in product form?

Answer 28

2cos((A + B)/2)cos((A - B)/2)

Question 29

What is cos(A) - cos(B) in product form?

Answer 29

-2sin((A + B)/2)sin((A - B)/2)