91Ó°ÊÓ

Use the sum-to-product formulas to find the exact value of the expression. $$\cos 120^{\circ}+\cos 60^{\circ}$$

Explain what would happen if you divided each side of the equation \(\cot x \cos ^{2} x=2 \cot x\) by \(\cot x .\) Is this a correct method to use when solving equations?

Use the trigonometric substitution to write the algebraic expression as a trigonometric function of \(\boldsymbol{\theta},\) where \(0<\boldsymbol{\theta}<\pi / 2\) $$\sqrt{4 x^{2}+9}, \quad 2 x=3 \tan \theta$$

Use the sum-to-product formulas to find the exact value of the expression. $$\cos \frac{3 \pi}{4}-\cos \frac{\pi}{4}$$

Use the sum-to-product formulas to find the exact value of the expression. $$\sin \frac{5 \pi}{4}-\sin \frac{3 \pi}{4}$$

Use the trigonometric substitution to write the algebraic expression as a trigonometric function of \(\boldsymbol{\theta},\) where \(0<\boldsymbol{\theta}<\pi / 2\) $$\sqrt{9 x^{2}+25}, \quad 3 x=5 \tan \theta$$

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

Use the trigonometric substitution to write the algebraic expression as a trigonometric function of \(\boldsymbol{\theta},\) where \(0<\boldsymbol{\theta}<\pi / 2\) $$\sqrt{2-x^{2}}, \quad x=\sqrt{2} \sin \theta$$

Explain in your own words how knowledge of algebra is important when solving trigonometric equations.

Use the trigonometric substitution to write the algebraic expression as a trigonometric function of \(\boldsymbol{\theta},\) where \(0<\boldsymbol{\theta}<\pi / 2\) $$\sqrt{10-x^{2}}, \quad x=\sqrt{10} \sin \theta$$