91Ó°ÊÓ

(a) Find all solutions of the equation. (b) Use a calculator to solve the equation in the interval \([0,2 \pi),\) correct to five decimal places. $$\sec x-5=0$$

47–52 Write the sum as a product. $$\sin 2 x-\sin 7 x$$

47–52 Write the sum as a product. $$\sin 3 x+\sin 4 x$$

(a) Use a graphing device to find all solutions of the equation, correct to two decimal places, and (b) find the exact solution. \(\sin ^{-1} x-\cos ^{-1} x=0\)

Verify the identity. $$ \sin ^{2} \alpha+\cos ^{2} \alpha+\tan ^{2} \alpha=\sec ^{2} \alpha $$

(a) Find all solutions of the equation. (b) Use a calculator to solve the equation in the interval \([0,2 \pi),\) correct to five decimal places. $$3 \sin x=7 \cos x$$

\(51-52\) (a) Graph the function and make a conjecture, then (b) prove that your conjecture is true. $$ y=-\frac{1}{2}[\cos (x+\pi)+\cos (x-\pi)] $$

(a) Find all solutions of the equation. (b) Use a calculator to solve the equation in the interval \([0,2 \pi),\) correct to five decimal places. $$5 \sin ^{2} x-1=0$$

An observer views the space shuttle from a distance of 2 miles from the launch pad. (a) Express the height of the space shuttle as a function of the angle of elevation \(\theta\) . (b) Express the angle of elevation \(\theta\) as a function of the height \(h\) of the space shuttle.

Verify the identity. $$ \tan ^{2} \theta-\sin ^{2} \theta=\tan ^{2} \theta \sin ^{2} \theta $$