91Ó°ÊÓ

Determine the values of the indicated functions in the given manner. Find \(\sin 120^{\circ}\) by using the functions of \(60^{\circ}\).

Solve the given trigonometric equations analytically (using identities when necessary for exact values when possible) for values of \(x\) for \(0 \leq x<2 \pi\). $$1-2 \cos x=0$$

Use the half-angle formulas to evaluate the given functions. $$\cos \frac{3 \pi}{8}$$

In Exercises \(7-12,\) multiply and simplify. In Exercises \(13-18,\) factor and simplify. $$\cos x(\tan x-\sec x)$$

Evaluate the given functions with the following information: \(\sin \alpha=4 / 5\) ( \(\alpha\) in first quadrant) and \(\cos \beta=-12 / 13(\beta\) in second quadrant). $$\sin (\alpha+\beta)$$

Determine the values of the indicated functions in the given manner. Find \(\tan 120^{\circ}\) by using the functions of \(60^{\circ}\).

Determine the values of the indicated functions in the given manner. Find \(\cos 60^{\circ}\) by using the functions of \(30^{\circ}\).

Solve the given trigonometric equations analytically (using identities when necessary for exact values when possible) for values of \(x\) for \(0 \leq x<2 \pi\). $$4 \tan x+2=3(1+\tan x)$$

Evaluate the given functions with the following information: \(\sin \alpha=4 / 5\) ( \(\alpha\) in first quadrant) and \(\cos \beta=-12 / 13(\beta\) in second quadrant). $$\tan (\beta-\alpha)$$

In Exercises \(7-12,\) multiply and simplify. In Exercises \(13-18,\) factor and simplify. $$\csc y(\sin y+3 \cos y)$$