91Ó°ÊÓ

Using Period to Evaluate sine and cosine In Exercises \(31-36\) , evaluate the trigonometric function using its period as an aid. $$\cos 3 \pi$$

Using Period to Evaluate sine and cosine In Exercises \(31-36\) , evaluate the trigonometric function using its period as an aid. $$\cos \frac{7 \pi}{3}$$

An Angle Formed by a line Through the Origin. The terminal side of \(\theta\) lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of \(\theta\) by finding a point on the line. $$\begin{array}{ll}{\text { Line }} & {\text { Quadrant }} \\ {4x+3y=0} & {\text { IV }}\end{array}$$

Navigation A ship leaves port at noon and has a bearing of \(\mathrm{S} 29^{\circ} \mathrm{W}\) . The ship sails at 20 \(\mathrm{knots.}\) (a) How many nautical miles south and how many nautical miles west will the ship have traveled by \(6 : 00\) P.M. (b) At \(6 : 00\) P.M., the ship changes course to due west. Find the ship's bearing and distance from the port of departure at \(7 : 00\) P.M.

Sketching the Graph of a Trigonometric Function In Exercises \(15-38\) , sketch the graph of the function. (Include two full periods.) $$y=2 \cot \left(x+\frac{\pi}{2}\right)$$

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

Trigonometric Function of a Quadrant Angle. Evaluate the trigonometric function of the quadrant angle, if possible. $$\cot \pi$$

Geometry Find the length of the sides of a regular pentagon inscribed in a circle of radius 25 inches.

Convert the angle measure from radians to degrees. Round to three decimal places. \(-0.57\)

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