Trig identities Flashcards by Isabelle Glaesman | Brainscape

Q

tan (x) =

A

sin(x) / cos(x)

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Q

cot(x)=

A

cos(x) / sin(x)

or

1/tan(x)

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Q

sec(x)=

A

1/cos(x)

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Q

csc(x)=

A

1/sin(x)

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Q

What is the Pythagorean identity?

A

sin^2(x) + cos^2(x)= 1

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Q

cos^2(x)=

A

1-sin^2(x)

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Q

sin^2(x)=

A

1-cos^2(x)

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Q

csc^2(x)=

A

1+cot^2(x)

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Q

sec^2(x)=

A

1+tan^2(x)

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Q

sin(2x)

A

2sin(x)cos(x)

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Q

cos(2x)

A

cos^2(x) - sin^2(x)

or

2cos^2(x)-1

or

1-2sin^2(x)

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Q

tan(2x)=

A

2tan(x) / (1-tan^2(x))

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Q

sin (x/2)=

A

√(1-cos(x)) / 2

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Q

cos (x/2) =

A

√(1+cos(x)) / 2

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Q

tan (x/2) =

A

(1-cos(x)) / sin(x)

sin(x) / (1+cos(x))

√(1-cos(x) / 1+ cos(x)

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Q

cos (A + B)

A

cos(A)cos(B)-sin(A)sin(B)

Q

sin (A+B)

A

sin (A)cos(B) - cos(A)sin(B)

Q

sin^2(x) (double angle)

A

1/2 (1-cos(2A))

Q

cos^2(A) (half angle) =

A

1/2 (1+cos(2A)

Q

Sin(A)sin(B) =

A

1/2 (cos(A-B) - cos(A+B))

Q

cos(A)cos(B)=

A

1/2 (cos(A-B)+cos(A+B))

Q

sinAcosB

A

1/2 (sin(A-B) + sin (A+B)

Q

sin’(x)

A

cos(x)

Q

cos’(x)

A

-sin (x)

Q

tan’ (X)

A

sec^2(x)

Q

sec’(x)

A

sec(x)tan(x)

Q

csc’(x)

A

-csc(x)cot(x)

Q

cot’(x)

A

-csc^2(x)

Q

∫sin(x) dx

A

-cos(x) + C

Q

∫ cos(x)dx

A

sin (x) +C

Q

∫ tan(x) dx=

A

ln|sec(x)| + C

Q

∫csc(x) dx

A

ln |csc(x) -cot(x)| +C

Q

∫sec(x) dx

A

ln |secx) + tan(x)| +C

Q

∫cot(x) dx

A

-ln |csc(x)| + C

Q

what is the range of arc cos, arc cot, arc sec ?

A

(0,π)

Q

what is the rang of arcsin, arctan, arc csc?

A

(π/2, -π/2)