91Ó°ÊÓ

Using a Calculator In Exercises \(43-48,\) use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) $$\cot (-0.9)$$

Finding a Reference Angle.Find the reference angle \(\theta^{\prime}\) and sketch \(\theta\) and \(\theta^{\prime}\) in standard position. $$\theta=-215^{\circ}$$

Harmonic Motion, find a model for simple harmonic motion satisfying the specified conditions. \(\begin{array}{ll}{\text { Displacement (\)t=0\() }} & {\text { Amplitude }} & {\text { Period }} \\ {3inches} & {3 \text { inches }} & {1.5 \text { seconds }}\end{array}\)

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

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

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

Sketching the Graph of a sine or cosine Function, sketch the graph of the function. (Include two full periods.) $$ y=3 \cos (x+\pi) $$

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

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 \((c) t=\frac{1}{2}\)

Solving a Trigonometric Equation Graphically In Exercises \(49-56\) , use a graph to solve the equation on the interval \(-2 \pi, 2 \pi\) $$\tan x=1$$