3.6 Modeling with trigonometric equations  (Page 11/14)

$\cos (3x)-{\cos }^{3}x=-\cos x{\sin }^{2}x-\sin x\sin (2x)$

$\frac{\tan \left(\frac{1}{2}x\right)+\tan \left(\frac{1}{8}x\right)}{1-\tan \left(\frac{1}{8}x\right)\tan \left(\frac{1}{2}x\right)}$

$\cos \left({\sin }^{-1}\left(0\right)-{\cos }^{-1}\left(\frac{1}{2}\right)\right)$

$\tan \left({\sin }^{-1}\left(0\right)+{\sin }^{-1}\left(\frac{1}{2}\right)\right)$

Find $\sin \left(2\theta \right),\cos \left(2\theta \right),$ and $\tan \left(2\theta \right)$ given $\cos \theta =-\frac{1}{3}$ and $\theta$ is in the interval $\left[\frac{\pi }{2},\pi \right].$

Find $\sin \left(2\theta \right),\cos \left(2\theta \right),$ and $\tan \left(2\theta \right)$ given $\sec \theta =-\frac{5}{3}$ and $\theta$ is in the interval $\left[\frac{\pi }{2},\pi \right].$

$\sin \left(\frac{7\pi }{8}\right)$

$\sec \left(\frac{3\pi }{8}\right)$

$\sin (2\beta ),\cos (2\beta ),\tan (2\beta ),\sin (2\alpha ),\cos (2\alpha ),\text{ and }\tan (2\alpha )$

$\sin \left(\frac{\beta }{2}\right),\cos \left(\frac{\beta }{2}\right),\tan \left(\frac{\beta }{2}\right),\sin \left(\frac{\alpha }{2}\right),\cos \left(\frac{\alpha }{2}\right),\text{ and }\tan \left(\frac{\alpha }{2}\right)$

$\frac{2\cos \left(2x\right)}{\sin \left(2x\right)}=\cot x-\tan x$

$\cot x\cos (2x)=-\sin (2x)+\cot x$

${\cos }^{2}x{\sin }^4(2x)$

${\tan }^{2}x{\sin }^{3}x$

$\cos \left(\frac{\pi }{3}\right)\sin \left(\frac{\pi }{4}\right)$

$2\sin \left(\frac{2\pi }{3}\right)\sin \left(\frac{5\pi }{6}\right)$

$2\cos \left(\frac{\pi }{5}\right)\cos \left(\frac{\pi }{3}\right)$

$\sin \left(\frac{\pi }{12}\right)-\sin \left(\frac{7\pi }{12}\right)$

$\cos \left(\frac{5\pi }{12}\right)+\cos \left(\frac{7\pi }{12}\right)$

$\sin (9x)\cos (3x)$

$\cos (7x)\cos (12x)$

$\sin (11x)+\sin (2x)$

$\cos (6x)+\cos (5x)$

$\tan x+1=0$

$2\sin (2x)+\sqrt{2}=0$

$2{\sin }^{2}x-\sin x=0$

${\cos }^{2}x-\cos x-1=0$

$2{\sin }^{2}x+5\sin x+3=0$

$\cos x-5\sin \left(2x\right)=0$

$\frac{1}{{\sec }^{2}x}+2+{\sin }^{2}x+4{\cos }^{2}x=0$

$\sqrt{3}{\cot }^{2}x+\cot x=1$

${\csc }^{2}x-3\csc x-4=0$

$20{\cos }^{2}x+21\cos x+1=0$

${\sec }^{2}x-2\sec x=15$

A man with his eye level 6 feet above the ground is standing 3 feet away from the base of a 15-foot vertical ladder. If he looks to the top of the ladder, at what angle above horizontal is he looking?

Using the ladder from the previous exercise, if a 6-foot-tall construction worker standing at the top of the ladder looks down at the feet of the man standing at the bottom, what angle from the horizontal is he looking?