91Ó°ÊÓ

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. $$ 4(\mathbf{u} \cdot \mathbf{v}) $$

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$a=5, c=2, B=90^{\circ}$$

Test for symmetry and then graph each polar equation. $$r=1-\sin \theta$$

In Exercises \(13-20\), let v be the vector from initial point \(P_{1}\) to terminal point \(P_{2} .\) Write \(\mathbf{v}\) in terms of \(\mathbf{i}\) and \(\mathbf{j}\) $$P_{1}=(-8,6), P_{2}=(-2,3)$$

Use a polar coordinate system like the one shown for Exercises 1–10 to plot each point with the given polar coordinates. $$ \left(3, \frac{4 \pi}{3}\right) $$

In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$ A=65^{\circ}, B=65^{\circ}, c=6 $$

In Exercises \(13-20\), let v be the vector from initial point \(P_{1}\) to terminal point \(P_{2} .\) Write \(\mathbf{v}\) in terms of \(\mathbf{i}\) and \(\mathbf{j}\) $$P_{1}=(-7,-4), P_{2}=(0,-2)$$

In Exercises \(11-26,\) plot each complex number. Then write the complex number in polar form. You may express the argument in degrees or radians. $$ -3 i $$

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$a=7, c=3, B=90^{\circ}$$

In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$ B=80^{\circ}, C=10^{\circ}, a=8 $$