91Ó°ÊÓ

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$A=56^{\circ}, C=24^{\circ}, a=22$$

In Exercises \(5-12,\) sketch each vector as a position vector and find its magnitude. $$\mathbf{v}=-4 \mathbf{i}$$

Plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. $$2+2 i$$

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$B=85^{\circ}, C=15^{\circ}, b=40$$

Let $$\mathbf{u}=2 \mathbf{i}-\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}+\mathbf{j}, \quad \text { and } \quad \mathbf{w}=\mathbf{i}+4 \mathbf{j}.$$ Find each specified scalar. $$\mathbf{u} \cdot \mathbf{v}+\mathbf{u} \cdot \mathbf{w}$$

Test for symmetry with respect to a. the polar axis. b. the line \(\theta=\frac{\pi}{2}\) c. the pole. $$r^{2}=16 \cos 2 \theta$$

Test for symmetry with respect to a. the polar axis. b. the line \(\theta=\frac{\pi}{2}\) c. the pole. $$r^{2}=16 \sin 2 \theta$$

In Exercises \(5-12,\) sketch each vector as a position vector and find its magnitude. $$\mathbf{v}=-5 \mathbf{j}$$

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$A=85^{\circ}, B=35^{\circ}, c=30$$

Let $$\mathbf{u}=2 \mathbf{i}-\mathbf{j}, \quad \mathbf{v}=3 \mathbf{i}+\mathbf{j}, \quad \text { and } \quad \mathbf{w}=\mathbf{i}+4 \mathbf{j}.$$ Find each specified scalar. $$\mathbf{v} \cdot \mathbf{u}+\mathbf{v} \cdot \mathbf{w}$$