MAT136H1 Lecture Notes - List Of Trigonometric Identities, Trigonometric Functions

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ultramarineeel914

16 Mar 2013

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MAT136H1 Full Course Notes

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Sine & cosine: odd power, when cosine power is odd, leave 1 cosine, convert all else to sine. Then let and solve using substitution: when sine power is odd: leave 1 sine, convert all else to cosine. Then let and solve using substitution: even power, when either cosine or sine power is even, use half-angle identities: ( ), and. Tangent & secant: odd power, when tangent power is odd: leave 1 of , convert all else to . Then let and , and solve by substitution: when cotangent power is odd: leave 1 of , convert all else to . Then let and , and solve by substitution: formulas for a single tangent, or a single secant, even power, when secant power is even: leave 1 of , convert all else to tangent based on the identity:

Related Questions

How do you find the integral of ?

To solve: The integral of

Formulas to be used: (in order of appearance in the Solution part below)

Trigonometric double-angle identity:
Difference rule of integration:
Constant multiple rule of integration:
Constant multiple rule of differentiation:
Trigonometric rule of integration:

Solution:

The given function has no direct integral, but can be solved by thinking of a trigonometric relationship that can be easily manipulated and integrated. In this case, the double-angle identity for cosine is used.