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=

Study These Flashcards

A

2sinθcosθ

Q

cos2θ=

Both cos and sin

Study These Flashcards

A

cos^2θ - sin^2θ

Q

cos2θ=

Just cos

Study These Flashcards

A

2cos^2θ - 1

Q

cos2θ=

Just sin

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A

1 - 2sin^2θ

tan2θ=

2tanθ ---------------- 1 - tan^2θ

sin(θ/2)=

+- root 1-cosθ/ 2

cos(θ/2)=

+- root 1 + cosθ/ 2

tan(θ/2)=

+- root 1 - cosθ/1 + cosθ

(Reducing powers) | sin^2x=

1 - cos2x ------------ 2

(Reducing powers) | cos^2x

1 + cos2x ------------ 2

(Reducing powers) | tan^2x=

1 - cos2x ------------ 1 + cos2x

(Co function identities) cosx=

sin(pi/2 - x) | sin(90• - x)

(Co function identities) | cotx=

tan(pi/2 - x) | tan(90• - x)

(Co function identities) | cscx=

sec(pi/2 - x) | sec(90• - x)

(Co function identities) sinx=

cos(pi/2 - x) | cos(90• - x)

(Co function identities) tanx=

cot(pi/2 - x) | cot(90• - x)

(Co function identities) secx=

csc(pi/2 - x) | csc(90• - x)

(Product sum identities) sinxcosy=

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

(Product sum identities) cosxsiny=

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

(Product sum identities) sinxsiny=

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

(Product sum identities) cosxcosy=

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

(Sum-product identities) sinx + siny=

2sin(x+y / 2)•cos(x-y / 2)

(Sum-product identities) sinx - siny=

2cos(x+y / 2) • sin(x-y / 2)

(Sum-product identities) cosx + cosy=

2cos(x+y / 2) • cos(x-y / 2)

(Sum-product identities) cosx - cosy=

-2sin(x+y / 2) • sin(x-y / 2)

Amplitude=

Max-min ------------ 2

Vertical shift (d)+

Max + min -------------- 2

B=

2pi ---- P

X'=

xcostheta - ysintheta

Y'=

xsintheta + ycostheta