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Finding a Reference Angle.Find the reference angle \(\theta^{\prime}\) and sketch \(\theta\) and \(\theta^{\prime}\) in standard position. $$\theta=-125^{\circ}$$

Graphing a Trigonometric Function In Exercises \(39-48\) , use a graphing utility to graph the function. (Include two full periods.) $$y=0.1 \tan \left(\frac{\pi x}{4}+\frac{\pi}{4}\right)$$

Harmonic Motion, find a model for simple harmonic motion satisfying the specified conditions. \(\begin{array}{ll}{\text { Displacement (\)t=0\() }} & {\text { Amplitude }} & {\text { Period }} \\ {0} & {4 \text { centimeters }} & {2 \text { seconds }}\end{array}\)

Using Trigonometric ldentities , use trigonometric identities to transform the left side of the equation into the right side \((0<\theta<\pi 2)\) . $$\tan \theta \cot \theta=1$$

Convert each angle measure to decimal degree form without using a calculator. Then check your answers using a calculator. (a) \(54^{\circ} 45^{\prime}\)

Using Trigonometric ldentities , use trigonometric identities to transform the left side of the equation into the right side \((0<\theta<\pi 2)\) . $$\cos \theta \sec \theta=1$$

Harmonic Motion, find a model for simple harmonic motion satisfying the specified conditions. \(\begin{array}{ll}{\text { Displacement (\)t=0\() }} & {\text { Amplitude }} & {\text { Period }} \\ {0} & {3 \text { meters }} & {6 \text { seconds }}\end{array}\)

Sketching the Graph of a sine or cosine Function, sketch the graph of the function. (Include two full periods.) $$ y=-10 \cos \frac{\pi x}{6} $$

Use the properties of inverse trigonometric functions to evaluate the expression. \(\tan (\arctan 45)\)

Graphing a Trigonometric Function In Exercises \(39-48\) , use a graphing utility to graph the function. (Include two full periods.) $$y=\frac{1}{3} \sec \left(\frac{\pi x}{2}+\frac{\pi}{2}\right)$$