MATH 13100 Lecture Notes - Lecture 5: Hypotenuse, Unit Circle, Even And Odd Functions

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20 Jun 2018

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MATH 131 Lecture Notes

Trigonometric Functions (0.7)

I. Review the right triangle and its sin, cos, and tan ratios below

The ratios are: inX ,cosX ,tanXs =opposite

hypotenuse = adjacent

hypotenuse = opposite

adjacent

II. We can also define trigonometric functions using the unit circle.

A. Sine is an odd function and cosine is an even function

III. Some general identities about sine and cosine

A. and in(− ) − in(t)s t =s os(− ) os(t)c t =c

1. Sine must flip, but cos stays the same. This is because changing the sign

will change the function vertically, and not necessarily horizontally.

B. and in( ) os(t)s2

π−t=c os( ) in(t)c2

π−t=s

C. in t os ts 2+c2= 1

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