91Ó°ÊÓ

Find the trigonometric function values. a) \(\sin \left(\frac{5 \pi}{12}\right)\) b) \(\cos \left(\frac{5 \pi}{12}\right)\) c) \(\tan \left(\frac{\pi}{12}\right)\) d) \(\sin \left(\frac{7 \pi}{12}\right)\) e) \(\cos \left(\frac{11 \pi}{12}\right)\) f) \(\sin \left(\frac{2 \pi}{3}\right)\) g) \(\sin \left(\frac{5 \pi}{6}\right)\) h) \(\cos \left(\frac{3 \pi}{4}\right)\) i) \(\tan \left(\frac{13 \pi}{12}\right)\) j) \(\cos \left(-\frac{\pi}{12}\right)\) k) \(\sin \left(\frac{11 \pi}{12}\right)\) l) \(\sin \left(\frac{29 \pi}{12}\right)\)

Simplify the function \(f\) using the addition and subtraction formulas. a) \(f(x)=\sin \left(x+\frac{\pi}{2}\right)\) b) \(f(x)=\cos \left(x-\frac{\pi}{4}\right)\) c) \(f(x)=\tan (\pi-x)\) d) \(f(x)=\sin \left(\frac{\pi}{6}-x\right)\) e) \(f(x)=\cos \left(x+\frac{11 \pi}{12}\right)\) f) \(f(x)=\cos \left(\frac{2 \pi}{3}-x\right)\)

Find the exact values of the trigonometric functions applied to the given angles by using the half-angle formulas. a) \(\cos \left(\frac{\pi}{12}\right)\) b) \(\tan \left(\frac{\pi}{8}\right)\) c) \(\sin \left(\frac{\pi}{24}\right)\) d) \(\cos \left(\frac{\pi}{24}\right)\) e) \(\sin \left(\frac{9 \pi}{8}\right)\) f) \(\tan \left(\frac{3 \pi}{8}\right)\) g) \(\sin \left(\frac{-\pi}{8}\right)\) h) \(\sin \left(\frac{13 \pi}{24}\right)\)

Find the exact values of the trigonometric functions of \(\frac{\alpha}{2}\) and of \(2 \alpha\) by using the half-angle and double angle formulas. a) \(\sin (\alpha)=\frac{4}{5},\) and \(\alpha\) in quadrant b) \(\cos (\alpha)=\frac{7}{13}\), and \(\alpha\) in quadrant IV c) \(\sin (\alpha)=\frac{-3}{5}\), and \(\alpha\) in quadrant III d) \(\tan (\alpha)=\frac{4}{3}\), and \(\alpha\) in quadrant III e) \(\tan (\alpha)=\frac{-5}{12}\), and \(\alpha\) in quadrant II f) \(\cos (\alpha)=\frac{-2}{3},\) and \(\alpha\) in quadrant II