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Magazine Problem 110
For the following exercises, simplify to one trigonometric expression. $$ 4 \sin \left(\frac{\pi}{8}\right) \cos \left(\frac{\pi}{8}\right) $$
Problem 111
For the following exercises, find the exact value using half-angle formulas. $$ \sin \left(\frac{\pi}{8}\right) $$
Problem 112
For the following exercises, find the exact value using half-angle formulas. $$ \cos \left(-\frac{11 \pi}{12}\right) $$
Problem 113
For the following exercises, find the exact value using half-angle formulas. $$ \sin \left(\frac{11 \pi}{12}\right) $$
Problem 114
For the following exercises, find the exact value using half-angle formulas. $$ \cos \left(\frac{7 \pi}{8}\right) $$
Problem 116
For the following exercises, find the exact value using half-angle formulas. $$ \tan \left(-\frac{3 \pi}{12}\right) $$
Problem 117
For the following exercises, find the exact value using half-angle formulas. $$ \tan \left(-\frac{3 \pi}{8}\right) $$
Problem 118
For the following exercises, find the exact values of a ) \(\sin \left(\frac{x}{2}\right),\) b) \(\sin \left(\frac{x}{2}\right),\) and \(c )\) without solving for \(x\) If \(\tan x=-\frac{4}{3},\) and \(x\) is in quadrant IV.
Problem 119
For the following exercises, find the exact values of a ) \(\sin \left(\frac{x}{2}\right),\) b) \(\sin \left(\frac{x}{2}\right),\) and \(c )\) without solving for \(x\) If \(\sin x=-\frac{12}{13}, \quad\) and \(x\) is in quadrant III.
Problem 120
For the following exercises, find the exact values of a ) \(\sin \left(\frac{x}{2}\right),\) b) \(\sin \left(\frac{x}{2}\right),\) and \(c )\) without solving for \(x\) If \(\csc x=7,\) and \(x\) is in quadrant II.
