91Ó°ÊÓ

In Exercises 83-86, use the trigonometric substitution to write the algebraic equation as a trigonometric function of \(\theta\), where \(-\pi / 2<\theta<\pi / 2\). Then find \(\sin \theta\) and \(\cos \theta\). $$ 3=\sqrt{36-x^{2}}, \quad x=6 \sin \theta $$

In Exercises 81-84, verify the identity. \(a \sin B \theta+b \cos B \theta=\sqrt{a^{2}+b^{2}} \cos (B \theta-C)\), where \(C=\arctan (a / b)\) and \(b>0\)

In Exercises 85-88, use reference angles to find the exact values of the sine, cosine, and tangent of the angle with the given measure. $$ 390^{\circ} $$

In Exercises 83-86, use the sum-to-product formulas to find the exact value of the expression. $$ \cos \frac{3 \pi}{4}-\cos \frac{\pi}{4} $$

In Exercises 83-86, use the trigonometric substitution to write the algebraic equation as a trigonometric function of \(\theta\), where \(-\pi / 2<\theta<\pi / 2\). Then find \(\sin \theta\) and \(\cos \theta\). $$ 2 \sqrt{2}=\sqrt{16-4 x^{2}}, \quad x=2 \cos \theta $$

In Exercises 85-88, use reference angles to find the exact values of the sine, cosine, and tangent of the angle with the given measure. $$ 600^{\circ} $$

In Exercises 83-86, use the trigonometric substitution to write the algebraic equation as a trigonometric function of \(\theta\), where \(-\pi / 2<\theta<\pi / 2\). Then find \(\sin \theta\) and \(\cos \theta\). $$ -5 \sqrt{3}=\sqrt{100-x^{2}}, \quad x=10 \cos \theta $$

In Exercises 83-86, use the sum-to-product formulas to find the exact value of the expression. $$ \sin \frac{5 \pi}{4}-\sin \frac{3 \pi}{4} $$

In Exercises 85-88, use reference angles to find the exact values of the sine, cosine, and tangent of the angle with the given measure. $$ -1845^{\circ} $$

In Exercises 87-90, find all solutions of the equation in the interval \([0,2 \pi)\). Use a graphing utility to graph the equation and verify the solutions. $$ \sin 6 x+\sin 2 x=0 $$