Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.6 Apply Sum and Difference Formulas - 14.6 Exercises - Skill Practice - Page 953: 39a

$a=r \cos \theta$ and $b=r \sin \theta$

The Trigonometric Identities are written as below: a) $\sin \theta=\dfrac{Opposite}{Hypotenuse}$ $\sin \theta=\dfrac{b}{r}$ This gives: $b=r \sin \theta$ b) $\cos \theta=\dfrac{Adjacent}{Hypotenuse}$ $\cos \theta=\dfrac{a}{r}$ This gives: $a=r \cos \theta$