Trig Identities Flashcards by Colin Hanley | Brainscape

Q

derivative of sin(x)

A

cos(x)

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Q

derivative of cos(x)

A

-sin(x)

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Q

integral of 1/(1+x^2)

A

arctanx

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Q

derivative of arctanx

A

1/(1+x^2)

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Q

derivative of tan(x)

A

sec(x)^2

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Q

integral of sec(x)^2

A

tan(x)

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Q

derivative of sec(x)

A

sec(x)tan(x)

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Q

integral of sec(x)tan(x)

A

sec(x)

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Q

derivative of tan(x)^2

A

2tan(x)sec(x)^2

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Q

integral of 2tan(x)sec(x)^2

A

tan(x)^2

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Q

derivative of sin(x)^2

A

2sin(x)cos(x)

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Q

integral of 2sin(x)cos(x)

A

sin(x)^2

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Q

derivative of csc(x)^2

A

-2cot(x)csc(x)^2

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Q

integral of -2cot(x)csc(x)^2

A

csc(x)^2

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Q

derivative of ln(x)

A

1/x

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Q

integral of 1/x

A

ln(x)

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Q

sec(x)^2=?

A

tan^2+1

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Q

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

A

1

Q

tan(x)^2

A

sec(x)^2-1

Q

sin(2x)

A

2sin(x)cos(x)

Q

cos(2x)

A

2cos(x)^2-1

Q

cos(x)^2

A

1+cos(2x)/2

Q

sin(x)^2

A

(1 - cos(2x))/2

Q

1 + cot²(x)

A

csc²(x)

Q

cot²(x)

A

csc²(x) - 1

Q

∫cos(x)dx

A

sin(x) + C

Q

∫sin(x)dx

A

-cos(x) + C

Q

∫sec²(x)dx

A

tan(x) + C

Q

∫csc²(x)dx

A

-cot(x) + C

Q

∫sec(x)tan(x)dx

A

sec(x) + C

Q

∫csc(x)cot(x)dx

A

-csc(x) + C

Q

∫tan(x)dx

A

ln|sec(x)| + C

Q

∫cot(x)dx

A

ln|sin(x)| + C

Q

∫sec(x)dx

A

ln|sec(x)-tan(x)| + C

Q

∫csc(x)dx

A

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

Q

√(a²-x²)

A

asinΘ

Q

√(x²+a²)

A

atanΘ

Q

√(x²-a²)

A

asecΘ

Q

odd power of sin/cos

A

split off sin(x), u = cos(x)

Q

even power of sin/cos

A

split off sin^2(x), use (1-cos2x)/2

Q

even power of sec

A

split off sec^2(x), u = tan(x)

Q

odd power of sec/tan

A

split of tan(x)sec(x), u = sec(x)

Q

A