trig identities Flashcards by Gail I

Q

cscx =

A

1/ sinx

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Q

secx =

A

1/ cosx

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Q

cotx =

A

1/ tanx

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Q

tanx =

A

sinx/ cosx

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Q

cotx =

A

cosx/ sinx

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Q

1 =

A

cos²x + sin²x

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Q

sec²x =

A

1 + tan²x

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Q

csc²x =

A

1 + cot²x

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Q

sin(-x) =

A

-sinx

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Q

cos(-x) =

A

cosx

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Q

tan(-x) =

A

-tanx

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Q

cos²x =

A

1 - sin²x

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Q

sin²x =

A

1 - cos²x

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Q

-sin²x =

A

cos²x - 1 → -1 + cos²x

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Q

sin(A + B)=

A

sinAcosB + cosAsinB

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Q

cos(A + B)=

A

cosAcosB - sinAsinB

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Q

tan(A + B)=

A

1 - tanAtanB

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Q

sin(A - B)=

A

sinAcosB - cosAsinB

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Q

cos(A - B)=

A

cosAcosB + sinAsinB

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Q

tan(A - B)=

A

1 + tanAtanB

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Q

sin2θ=

A

2sinθcosθ

Q

cos2θ=

Both cos and sin

A

cos^2θ - sin^2θ

Q

cos2θ=

Just cos

A

2cos^2θ - 1

Q

cos2θ=

Just sin

A

1 - 2sin^2θ

Q

tan2θ=

A

1 - tan^2θ

Q

sin(θ/2)=

A

+- root 1-cosθ/ 2

Q

cos(θ/2)=

A

+- root 1 + cosθ/ 2

Q

tan(θ/2)=

A

+- root 1 - cosθ/1 + cosθ

Q

(Reducing powers)

sin^2x=

A

Q

(Reducing powers)

cos^2x

A

Q

(Reducing powers)

tan^2x=

A

1 + cos2x

Q

(Co function identities)

cosx=

A

sin(pi/2 - x)

sin(90• - x)

Q

(Co function identities)

cotx=

A

tan(pi/2 - x)

tan(90• - x)

Q

(Co function identities)

cscx=

A

sec(pi/2 - x)

sec(90• - x)

Q

(Co function identities)

sinx=

A

cos(pi/2 - x)

cos(90• - x)

Q

(Co function identities)

tanx=

A

cot(pi/2 - x)

cot(90• - x)

Q

(Co function identities)

secx=

A

csc(pi/2 - x)

csc(90• - x)

Q

(Product sum identities)

sinxcosy=

A

1/2[sin(x+y) + sin(x+y)]

Q

(Product sum identities)

cosxsiny=

A

1/2[sin(x+y) - sin(x-y)]

Q

(Product sum identities)

sinxsiny=

A

1/2[cos(x-y) - cos(x+y)]

Q

(Product sum identities)

cosxcosy=

A

1/2[cos(x+y) + cos(x-y)]

Q

(Sum-product identities)

sinx + siny=

A

2sin(x+y / 2)•cos(x-y / 2)

Q

(Sum-product identities)

sinx - siny=

A

2cos(x+y / 2) • sin(x-y / 2)

Q

(Sum-product identities)

cosx + cosy=

A

2cos(x+y / 2) • cos(x-y / 2)

Q

(Sum-product identities)

cosx - cosy=

A

-2sin(x+y / 2) • sin(x-y / 2)

Q

Amplitude=

A

2

Q

Vertical shift (d)+

A

2

Q

B=

A

P

Q

X’=

A

xcostheta - ysintheta

Q

Y’=

A

xsintheta + ycostheta