91Ó°ÊÓ

Solve each equation for solutions over the interval \(\left[0^{\circ}, 360^{\circ}\right) .\) Give solutions to the nearest tenth as appropriate. $$8 \cos ^{2} \theta+18 \cos \theta=5$$

How can you determine that the equation \((\cos \theta-4)(\sin \theta+5)=0\) has no solutions by simply knowing the ranges of the sine and cosine functions?

Use a half-number identity to find an expression for the exact value for each function, given the information about \(x\). $$\cos \frac{x}{2}, \text { given cot } x=-3 \text { and } \frac{\pi}{2} < x < \pi$$

Suppose that A and B are angles in standand position. Use the given information to find (a) \(\sin (A+B)\), (b) \(\sin (A-B)\), (c) \(\tan (A+B)\), (d) \(\tan (A-B)\), (e) the quadrant of \(A+B\), and ( \(f\) ) the quadrant of \(A-B\). Do not use a calculator. $$\sin A=\frac{3}{5}, \sin B=-\frac{12}{13}, \quad 0

Use a calculator to give each value of \(\theta\) in decimal degrees. $$\theta=\cos ^{-1}(-0.13348816)$$

Write expression in terms of sine and cosine, and simplify it. (The final expression does not have to be in terms of sine and cosine.) $$\cot ^{2} \theta\left(1+\tan ^{2} \theta\right)$$

Write expression in terms of sine and cosine, and simplify it. (The final expression does not have to be in terms of sine and cosine.) $$\sin ^{2} \theta\left(\csc ^{2} \theta-1\right)$$

Use a calculator to give each value of \(\theta\) in decimal degrees. $$\theta=\arccos (-0.39876459)$$

For individual or group investigation. Write the equation \(\tan ^{3} x=3 \tan x\) with 0 on one side.

Suppose that A and B are angles in standand position. Use the given information to find (a) \(\sin (A+B)\), (b) \(\sin (A-B)\), (c) \(\tan (A+B)\), (d) \(\tan (A-B)\), (e) the quadrant of \(A+B\), and ( \(f\) ) the quadrant of \(A-B\). Do not use a calculator. $$\cos A=-\frac{8}{17}, \cos B=-\frac{3}{5}, \quad \pi