Trig Identities

Question 1

1 = (sin)

Answer 1

Sin^2 θ + cos^2 θ

Question 2

1 = (cos)

Answer 2

Sin^2 θ + cos^2 θ

Question 3

1 = (sec)

Answer 3

Sec^2 θ - tan^2 θ

Question 4

1 = (tan)

Answer 4

Sec^2 θ - tan^2 θ

Question 5

1 = (csc)

Answer 5

Csc^2 θ - cot^2 θ

Question 6

1 = (cot)

Answer 6

Csc^2 θ - cot^2 θ

Question 7

Cos θ

Answer 7

Sin(pi/2 - θ)

Question 8

Cot θ

Answer 8

Tan(pi/2 - θ)

Question 9

Sec θ

Answer 9

Csc(pi/2 - θ)

Question 10

Sin θ

Answer 10

Cos(pi/2 - θ)

Question 11

Tan θ

Answer 11

Cot(pi/2 - θ)

Question 12

Csc θ

Answer 12

Sec(pi/2 - θ)

Question 13

Sin(2θ)

Answer 13

2sinθ cosθ

Question 14

Cos(2θ) (cos &sin)

Answer 14

Cos^2 θ - sin^2 θ

Question 15

Cos(2θ) (cos)

Answer 15

2cos^2 θ -1

Question 16

Cos(2θ) (sin)

Answer 16

1-2sin^2 θ

Question 17

Tan(2θ)

Answer 17

(2 tanθ)/(1-tan^2 θ)

Question 18

Sin(θ/2)

Answer 18

±√((1-cos θ)/2)

Question 19

Cos(θ/2)

Answer 19

±√((1+cos θ)/2)

Question 20

Tan(θ/2) (cos only)

Answer 20

±√((1-cos θ)/(1+cos θ))

Question 21

Tan(θ/2) (sin & cos)

Answer 21

(Sin θ)/(1+cos θ)

Question 22

Sin^2 θ

Answer 22

(1-cos(2θ))/2

Question 23

Cos^2 θ

Answer 23

(1+cos(2θ))/2

Question 24

Tan^2 θ

Answer 24

(1-cos(2θ))/(1+cos(2θ)

Question 25

Sin(θ ± α)

Answer 25

Sin θ cos α ± cos θ sin α

Question 26

Cos(θ ± α)

Answer 26

Cos θ cos α ∓ sin θ sin α