91Ó°ÊÓ

In Exercises \(7-22,\) sketch the graphs of the polar equations. $$r=-2 \cos \theta$$

Solve the given triangles. The standard notation for labeling of triangles is used. Round all answers to four decimal places. $$B=63.7^{\circ}, C=48^{\circ}, b=33$$

Convert each of the given pairs of polar coordinates to a pair of rectangular coordinates. $$\left(-1, \frac{\pi}{6}\right)$$

Find \(\mathbf{u}-\mathbf{v}, \mathbf{u}+2 \mathbf{v},\) and \(-3 \mathbf{u}+\mathbf{v}\). $$\mathbf{u}=-2 \mathbf{i}+3 \mathbf{j}, \mathbf{v}=4 \mathbf{i}-\mathbf{j}$$

Solve the given triangles. The standard notation for labeling of triangles is used. Round all answers to four decimal places. $$C=52.1^{\circ}, A=73^{\circ}, a=15$$

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

Calculate projev. Then decompose \(\mathbf{v}\) into \(\mathbf{v}_{1}\) and \(\mathbf{v}_{2},\) where \(\mathbf{v}_{1}\) is parallel to \(\mathbf{w}\) and \(\mathbf{v}_{2}\) is orthogonal to \(\mathbf{w}\) $$\mathbf{v}=\langle 6,12\rangle, \mathbf{w}=\langle 3,1\rangle$$

Express each complex number in trigonometric form. $$2 \sqrt{3}-2 i$$

Convert each of the given pairs of polar coordinates to a pair of rectangular coordinates. $$-\left(2, \frac{2 \pi}{3}\right)$$

Solew the given triangles. The standard notation for labeling of triangles is used. Round answers to four decimal places. $$a=6, c=16, B=111^{\circ}$$