Section 7.2

7.2 Trigonometric Integrals

Key Concepts

The primary tool are the identities :

sin²(x) = 1/2(1-cos(2x))
cos²(x) = 1/2(1+cos(2x))

These allow even powers of sin(x) and cos(x) to be reduced to first power terms.
Other useful identities are:

sec²(x) = 1 + tan²(x)
tan²(x) = sec²(x) -1

and

sin(A) cos(B) = 1/2[sin(A-B) + sin(A+B)]
sin(A) sin(B) = 1/2[cos(A-B) - cos(A+B)]
cos(A) cos(B) = 1/2[cos(A-B) + cos(A+B)]

Using the identities given above, products of powers of trigonometric functions can be calculated.

Note: Consult Appendix E of the text for a fairly complete list of trigonometric integrals.

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