Trig Identities

Question 1

Reciprocal Identity : sinθ =

Answer 1

1/cscθ

Question 2

Reciprocal Identity : cosθ =

Answer 2

1/secθ

Question 3

Reciprocal Identity : tanθ =

Answer 3

1/cotθ

Question 4

Quotient Identity: tanθ =

Answer 4

sinθ/cosθ

Question 5

Quotient Identity: cotθ =

Answer 5

cosθ/sinθ

Question 6

Pythagorean Trig Identity: sin²θ + cos²θ =

Answer 6

1

Question 7

Pythagorean Trig Identity: 1 + cot²θ =

Answer 7

csc²θ

Question 8

Pythagorean Trig Identity: tan²θ + 1 =

Answer 8

sec²θ

Question 9

odd functions

Answer 9

sin(-x) = -sin(x)

csc(-x) = -csc(x)

tan(-x) = -tan(x)

cot(-x) = -cot(x)

Question 10

even functions

Answer 10

cos(-x) = cos(x)

sec(-x) = sec(x)

Question 11

Cofunction : sin(90°-x) =

Answer 11

cos(x)

Question 12

Cofunction : cos(90°-x) =

Answer 12

sin(x)

Question 13

Cofunction : tan(90°-x) =

Answer 13

cot(x)

Question 14

Cofunction : csc(90°-x) =

Answer 14

sec(x)

Question 15

Cofunction : sec(90°-x) =

Answer 15

csc(x)

Question 16

Cofunction : cot(90°-x) =

Answer 16

tan(x)

Question 17

Sum and Difference : sin(A+B)=

Answer 17

sinAcosB+sinBcosA

Question 18

Sum and Difference : sin(A-B)=

Answer 18

sinAcosB-sinBcosA

Question 19

Sum and Difference : cos(A+B)=

Answer 19

cosAcosB-sinAsinB

Question 20

Sum and Difference : cos(A-B)=

Answer 20

cosAcosB+sinAsinB

Question 21

Sum and Difference : tan(A+B)=

Answer 21

tanA+tanB/1-tanAtanB

Question 22

Sum and Difference : tan(A-B)=

Answer 22

tanA-tanB/1+tanAtanB

Question 23

Double Angle : sin(2x) =

Answer 23

2sinxcosx

Question 24

Double Angle : cos(2x) =

Answer 24

cos²θ-sin²θ

2cos²θ-1

1-2sin²θ

Question 25

Double Angle : tan(2x) =

Answer 25

2tanx/1-tan²x

Question 26

Half Angle: sin(x/2)

Answer 26

±√((1-cosx)/2)

Question 27

Half Angle: cos(x/2)

Answer 27

±√((1+cosx)/2)

Question 28

Half Angle: tan(x/2)

Answer 28

±√(1-cosx)/(1+cosx)

(1-cosx)/sinx

sinx/(1+cosx)