PROVE: A reduction formula is one that can be used to "reduce" the number of terms in the input for a trigonometric function. explain the figure shows that the following reduction formulas are valid:
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PROVE More reduction formulas by the Angle-side-Angle Theorem from elementary geometry, triangles CDO, and AOB in the figure to the right arc congruent. Explain how this proves that if B has coordinates (x,y), then D has coordinates (-y,x). Then explain how the figure shows that the following reduction formulas are valid.
Use the chain Rule to show that if is measured in degrees, then
(This gives one reason for the convention that radian measure is always used when dealing with trigonometric functions in calculus: the differentiation formulas would not be as simple if we used degree measure.)
In the right triangle shown, explain why . Explain how you can obtain all six cofunction identities from this triangle for .
Note that and are complementary angles. So the cofunction identities state that "a trigonometric function of an angle is equal to the corresponding cofunction of the complementary angle ."
is measured in degrees, then
