91Ó°ÊÓ

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). $$\tan (\beta-\alpha)$$

Solve the given trigonometric equations analytically (using identities when necessary for exact values when possible) for values of \(x\) for \(0 \leq x<2 \pi\). $$4-\sec ^{2} x=0$$

Simplify the given expressions by giving the results in terms of one-half the given angle. Then use a calculator to verify the result. $$\sqrt{\frac{1-\cos 236^{\circ}}{2}}$$

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). $$\cos (\alpha+\beta)$$

In Exercises \(7-12,\) multiply and simplify. In Exercises \(13-18,\) factor and simplify. $$\cos \theta \cot \theta(\sec \theta-2 \tan \theta)$$

Simplify the given expressions by giving the results in terms of one-half the given angle. Then use a calculator to verify the result. $$\sqrt{\frac{1+\cos 98^{\circ}}{2}}$$

In Exercises \(7-12,\) multiply and simplify. In Exercises \(13-18,\) factor and simplify. $$(\csc x-1)(\csc x+1)$$

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

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). $$\sin (\alpha-\beta)$$

Use a calculator to verify the values found by using the double-angle formulas. Find \(\cos 96^{\circ}\) directly and by using functions of \(48^{\circ}\).