Trig Identities Flashcards

1
Q

Reciprocal Identity : sinθ =

A

1/cscθ

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2
Q

Reciprocal Identity : cosθ =

A

1/secθ

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3
Q

Reciprocal Identity : tanθ =

A

1/cotθ

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4
Q

Quotient Identity: tanθ =

A

sinθ/cosθ

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5
Q

Quotient Identity: cotθ =

A

cosθ/sinθ

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6
Q

Pythagorean Trig Identity: sin²θ + cos²θ =

A

1

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7
Q

Pythagorean Trig Identity: 1 + cot²θ =

A

csc²θ

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8
Q

Pythagorean Trig Identity: tan²θ + 1 =

A

sec²θ

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9
Q

odd functions

A

sin(-x) = -sin(x)

csc(-x) = -csc(x)

tan(-x) = -tan(x)

cot(-x) = -cot(x)

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10
Q

even functions

A

cos(-x) = cos(x)

sec(-x) = sec(x)

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11
Q

Cofunction : sin(90°-x) =

A

cos(x)

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12
Q

Cofunction : cos(90°-x) =

A

sin(x)

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13
Q

Cofunction : tan(90°-x) =

A

cot(x)

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14
Q

Cofunction : csc(90°-x) =

A

sec(x)

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15
Q

Cofunction : sec(90°-x) =

A

csc(x)

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16
Q

Cofunction : cot(90°-x) =

A

tan(x)

17
Q

Sum and Difference : sin(A+B)=

A

sinAcosB+sinBcosA

18
Q

Sum and Difference : sin(A-B)=

A

sinAcosB-sinBcosA

19
Q

Sum and Difference : cos(A+B)=

A

cosAcosB-sinAsinB

20
Q

Sum and Difference : cos(A-B)=

A

cosAcosB+sinAsinB

21
Q

Sum and Difference : tan(A+B)=

A

tanA+tanB/1-tanAtanB

22
Q

Sum and Difference : tan(A-B)=

A

tanA-tanB/1+tanAtanB

23
Q

Double Angle : sin(2x) =

A

2sinxcosx

24
Q

Double Angle : cos(2x) =

A

cos²θ-sin²θ

2cos²θ-1

1-2sin²θ

25
Q

Double Angle : tan(2x) =

A

2tanx/1-tan²x

26
Q

Half Angle: sin(x/2)

A

±√((1-cosx)/2)

27
Q

Half Angle: cos(x/2)

A

±√((1+cosx)/2)

28
Q

Half Angle: tan(x/2)

A

±√(1-cosx)/(1+cosx)

(1-cosx)/sinx

sinx/(1+cosx)