91Ó°ÊÓ

Use a graph to solve the equation on the interval \(-2 \pi, 2 \pi\). $$\tan x=1$$

Sketch the graph of the function. (Include two full periods.) $$y=3 \cos (x+\pi)$$

Converting to \(\mathrm{D}^{\circ} \mathrm{M}^{\prime} \mathrm{S}^{\prime \prime}\) Form \(\quad\) Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(240.6^{\circ}\) (b) \(-145.8^{\circ}\)

Find the reference angle \(\boldsymbol{\theta}^{\prime}\) and sketch \(\boldsymbol{\theta}\) and \(\boldsymbol{\theta}^{\prime}\) in standard position. $$\theta=\frac{2 \pi}{3}$$

Use the properties of inverse trigonometric functions to evaluate the expression. $$\cos [\arccos (-0.1)]$$

Harmonic Motion The displacement from equilibrium of an oscillating weight suspended by a spring is given by \(y(t)=\frac{1}{4} \cos 6 t\) where \(y\) is the displacement (in feet) and \(t\) is the time (in seconds). Find the displacement when (a) \(t=0\)(b) \(t=\frac{1}{4},\) and \((\mathrm{c}) t=\frac{1}{2}\)

Use trigonometric identities to transform the left side of the equation into the right side \((0<\theta<\pi 2)\). $$\tan \alpha \cos \alpha=\sin \alpha$$

Converting to \(\mathrm{D}^{\circ} \mathrm{M}^{\prime} \mathrm{S}^{\prime \prime}\) Form \(\quad\) Convert each angle measure to degrees, minutes, and seconds without using a calculator. Then check your answers using a calculator. (a) \(-345.12^{\circ}\) (b) \(-3.58^{\circ}\)

Find a model for simple harmonic motion satisfying the specified conditions. Displacement \((t=0)\) 2 feet Amplitude 2 feet Period 10 seconds

Sketch the graph of the function. (Include two full periods.) $$y=\sin (x-2 \pi)$$