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Trigonometric and Integration Formulas

This document contains a list of trigonometric identities and formulas for integration. There are over a dozen trig identities listed along with basic integration formulas involving trigonometric, exponential, logarithmic and inverse trig functions.

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Sarah Mae Bautista
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© © All Rights Reserved
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67 views2 pages

Trigonometric and Integration Formulas

This document contains a list of trigonometric identities and formulas for integration. There are over a dozen trig identities listed along with basic integration formulas involving trigonometric, exponential, logarithmic and inverse trig functions.

Uploaded by

Sarah Mae Bautista
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Reciprocal Identities Sum and Difference Identities

1 1 sin (A ± B) = sin A cos B ± cos A sin B


sin θ = csc θ =
csc θ sin θ
cos (A ± B) = cos A cos B ∓ sin A sin B
1 1
cos θ = sec θ = tan A ± tan B
sec θ cos θ tan (A ± B) =
1 ∓ tan A tan B
1 1
tan θ = cot θ =
cot θ tan θ Double-Angle Identities

Quotient Identities sin 2θ = 2 sin θ cos θ

sin θ cos 2θ = cos2 θ − sin2 θ


= tan θ = 2 cos2 θ − 1
cos θ
= 1 − 2 sin2 θ
cos θ
= cot θ
sin θ 2 tan θ
tan 2θ =
1 − tan2 θ
Pythagorean Identities
Power reduction formulae
2 2
sin θ + cos θ = 1 1 − cos 2θ
sin2 θ =
2
tan2 θ + 1 = sec2 θ 1 + cos 2θ
cos2 θ =
2
1 + cot2 θ = csc2 θ
Half-Angle Identities
r
Co-function Identities θ 1 − cos θ
sin = ±
π  π  2 2
r
sin θ = cos −θ cos θ = sin −θ θ 1 + cos θ
2 2 cos = ±
2 2
π  π  r
tan θ = cot −θ cot θ = tan −θ θ 1 − cos θ
2 2 tan = ± 6 1
, cos θ =
2 1 + cos θ
π  π 
sec θ = csc −θ csc θ = sec −θ
2 2 Product-Sum Identities
1
Opposite Angle Identities sin A cos B = [sin (A + B) + sin (A − B)]
2
1
sin(−θ ) = − sin θ cos A sin B = [sin (A + B) − sin (A − B)]
2
1
sin A sin B = [cos (A − B) − cos (A + B)]
cos(−θ ) = cos θ 2
1
cos A cos B = [cos (A + B) + cos (A − B)]
2
tan(−θ ) = − tan θ
Basic Integration Formulae
ˆ ˆ
xn+1 1
1. xn dx = +C (n 6= 1) 2. dx = ln |x| +C
n+1 x

ˆ ˆ
ax
3. x x
e dx = e +C 4. ax dx = +C
ln a

ˆ ˆ
5. sin x dx = − cos x +C 6. cos x dx = sin x +C

ˆ ˆ
7. sec2 x dx = tan x +C 8. csc2 x dx = − cot x +C

ˆ ˆ
9. sec x tan x dx = sec x +C 10. csc x cot x dx = − csc x +C

ˆ ˆ
11. sec x dx = ln | sec x + tan x| +C 12. csc x dx = ln | csc x − cot x| +C

ˆ ˆ
13. tan x dx = ln | sec x| +C 14. cot x dx = ln | sin x| +C

ˆ ˆ
dx 1 x dx −1 x
 
15. = tan−1 +C 16. √ = sin +C, a > 0
2
x +a 2 a a a2 − x2 a

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