Trigonometric Integrals
ο»ΏTrigonometric Integrals
Part 1: Some Prep Work
J. Gonzalez-Zugasti, University of Massachusetts - Lowell
1
sin2 and cos2
Recall:
sin2
=
1
-
cos 2
2
=
1 2
-
1 4
sin
2
+
and
cos2
=
1
+
cos 2
2
=
1 2
+
1 4
sin
2
+
J. Gonzalez-Zugasti, University of Massachusetts - Lowell
2
Evaluate
Example 1
cos3
Solution: Use sin2 + cos2 = 1 cos2 = 1 - sin2 .
J. Gonzalez-Zugasti, University of Massachusetts - Lowell
3
Example 1 (continued)
cos3 = cos2 cos
= 1 - sin2 cos
= 1 - 2
= sin = cos
=
-
1 3
3
+
=
sin
-
1 3
sin3
+
J. Gonzalez-Zugasti, University of Massachusetts - Lowell
4
Evaluate
Example 2
sin4
Solution:
Use
sin2
=
1-cos 2
2
and
cos2
=
1+cos 2
2.
J. Gonzalez-Zugasti, University of Massachusetts - Lowell
5
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