91Ó°ÊÓ

Solve the given trigonometric equation on \(0^{\circ} \leq \theta<360^{\circ}\) and express the answer in degrees to two decimal places. $$5 \cot \theta-9=0$$

Verify each of the trigonometric identities. $$\frac{2-\sin ^{2} x}{\cos x}=\sec x+\cos x$$

Use a calculator to evaluate each expression. Give the answer in radians and round it to two decimal places. $$\cos ^{-1}(0.1423)$$

Graph the functions. $$y=\sin (2 x) \cos (2 x)$$

Optics. Two optical signals with uniform \((A=1)\) intensities and wavelengths of \(1.55 \mu \mathrm{m}\) and \(0.63 \mu \mathrm{m}\) are "beat" together. What is the resulting sum if their individual signals are given by \(\sin \left(\frac{2 \pi t c}{1.55 \mu \mathrm{m}}\right)\) and \(\sin \left(\frac{2 \pi t c}{0.63 \mu \mathrm{m}}\right)\) where \(c=3.0 \times 10^{8} \mathrm{m} / \mathrm{s} ?\left(\text { Note: } 1 \mu \mathrm{m}=10^{-6} \mathrm{m} .\right)\)

Verify each of the trigonometric identities. $$\frac{2-\cos ^{2} x}{\sin x}=\csc x+\sin x$$

Graph the functions. $$y=3 \sin (3 x) \cos (-3 x)$$

Determine whether each equation is a conditional equation or an identity. $$\cos (A+B)=\cos A+\cos B$$

Solve the given trigonometric equation on \(0^{\circ} \leq \theta<360^{\circ}\) and express the answer in degrees to two decimal places. $$5 \sec \theta+6=0$$

Use a calculator to evaluate each expression. Give the answer in radians and round it to two decimal places. $$\tan ^{-1}(-0.9279)$$