91Ó°ÊÓ

Graph each of the given vectors in standard position. $$\langle 1,0\rangle$$

For what value(s) of \(\theta\) in \([0,2 \pi]\) does \(\cos \theta\) reach a minimum value?

Determine the quadrant where the terminal side of each angle lies. $$\theta=\frac{11 \pi}{6}$$

Find \(r\) for the given complex numbers. $$3 i$$

In Exercises \(7-22,\) sketch the graphs of the polar equations. $$\theta=\frac{2 \pi}{3}$$

Find the magnitude and direction of each of the given vectors. Express the direction as an angle \(\theta\) in standard position, where \(0^{\circ} \leq \theta<360^{\circ},\) to tuo decimal places. $$\mathbf{w}=\langle 3,5\rangle$$

Find the magnitude and direction of each of the given vectors. Express the direction as an angle \(\theta\) in standard position, where \(0^{\circ} \leq \theta<360^{\circ},\) to tuo decimal places. $$\mathbf{v}=1 \mathbf{i}+2.5 \mathbf{j}$$

Hiking A group of people go hiking. On the first leg, they hike 2.5 miles due north. The direction of the second and final leg is \(\mathrm{N} 36^{\circ} \mathrm{E}\). If they end up at a place that is 5.8 miles from their starting point, how great a distance did they traverse? Sketch a figure first.

In Exercises \(31-46,\) sketch the graphs of the polar equations. $$r^{2}=9 \sin (2 \theta)$$

Geometry Marisa has a triangular sign made with her last name on it. She has the sign attached to her lamppost so that visitors can easily identify her house. The lengths of two edges of the sign are 10 inches and 7 inches, and the angle opposite the 10 -inch edge is \(75^{\circ} .\) What is the length of the third edge?