91Ó°ÊÓ

Angle of Elevation. If a 7-foot lamppost makes a 10 -foot shadow on the sidewalk, find its angle of elevation to the sun.

In Exercises 69-88, evaluate each expression exactly. $$ \sin \left[\cos ^{-1}\left(\frac{2}{3}\right)\right] $$

Solve for the smallest positive \(x\) that makes this statement true: $$ \cos x \cos 15^{\circ}+\sin x \sin 15^{\circ}=0.7 $$

Angle of Elevation. If a 6-foot lamppost makes an 8 -foot shadow on the sidewalk, find its angle of elevation to the sun.

Find the exact value of the solutions to the equation \(\cos \left(\frac{1}{2} x\right)=\cos x\) on the interval \([0,2 \pi)\)

In Exercises 69-88, evaluate each expression exactly. $$ \sin \left[\tan ^{-1}\left(\frac{12}{5}\right)\right] $$

In Exercises \(71-74\), explain the mistake that is made. Find all solutions to the equation \(\sin \theta=\frac{3}{5}\) on \(0^{\circ} \leq \theta<360^{\circ}\). Solution: Write in equivalent inverse notation. \(\theta=\sin ^{-1}\left(\frac{3}{5}\right)\) Use a calculator to approximate inverse sine. \(\theta=36.87^{\circ}\) This is incorrect. What mistake was made?

In Exercises 69-88, evaluate each expression exactly. $$ \cos \left[\tan ^{-1}\left(\frac{7}{24}\right)\right] $$

Find the exact value of the solutions to the equation \(\tan \left(\frac{1}{2} x\right)=\sin x\) on the interval \([0,2 \pi)\).

Solve the inequality exactly: $$ -\frac{1}{4} \leq \sin x \cos x \leq \frac{1}{4} \text { on the interval }[0, \pi) $$