Use the graph. Find the direction angle of $\mathbf{v}$, measured counterclockwise from the positive $x$-axis on $\left[0^{\circ },360^{\circ }\right)$.

Let $\mathbf{r}=⟨3,3⟩$ and $\mathbf{s}=⟨-4,-8⟩$. Find $\mathbf{r}\cdot \mathbf{s}$.

Use the graph. Write $\mathbf{q}$ in the form $a\mathbf{i}+b\mathbf{j}$.

How many petals does the graph of $r=5\sin (6\theta )$ have, and how far does each reach from the pole?

Let $\mathbf{u}=⟨7,-5⟩$ and $\mathbf{v}=⟨2,-1⟩$. Find $\mathbf{u}\cdot \mathbf{v}$.

Write $x^2+y^2=3x$ as a polar equation.

Use the graph. Find the magnitude of $\mathbf{a}$.

Describe the graph of $r=-4\cos \theta$.

Use the graph. Convert point $P$ to rectangular coordinates, in exact form.

A vector has magnitude $16$ and direction angle $240^{\circ }$. Write it in component form, in simplest radical form.

Use the graph. Convert point $P$ to rectangular coordinates, in exact form.

Which statement about $\mathbf{u}=⟨-5,-1⟩$ and $\mathbf{v}=⟨1,1⟩$ is correct?

Convert $r=8\cos \theta$ to a rectangular equation.

What is the argument of the complex number $z=9\sqrt{3}+9i$ on $\left[0^{\circ },360^{\circ }\right)$?

The two square roots of $16\left(\cos 270^{\circ }+i\sin 270^{\circ }\right)$ are each written with an argument on $\left[0^{\circ },360^{\circ }\right)$. Which one has the smallest argument?

How many petals does the graph of $r=7\cos (6\theta )$ have, and how far does each reach from the pole?

Which of these limacons is dimpled, with no inner loop?

Write $z=-5+5i\sqrt{3}$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.

For $\mathbf{w}=⟨7,-3⟩$, find $\mathbf{w}\cdot \mathbf{w}$.

Which statement about $\mathbf{u}=⟨6,-8⟩$ and $\mathbf{v}=⟨2,5⟩$ is correct?

Use the graph. Find the magnitude of $\mathbf{w}$.

Which curve does $r=2\cos (3\theta )$ trace?

Convert $r=4\csc \theta$ to a rectangular equation.

Use the graph. Find the magnitude of $\mathbf{r}$.

Find the vector of magnitude $52$ that points in the same direction as $\mathbf{v}=⟨-5,12⟩$.

Use the graph. Write $\mathbf{v}$ in component form.

Use the graph. Find the unit vector in the direction of $\mathbf{p}$.

For what value of $k$ are $⟨k,6⟩$ and $⟨8,9⟩$ orthogonal?

Find the vector of magnitude $20$ that points in the same direction as $\mathbf{r}=⟨-3,-4⟩$.

Use De Moivre's theorem to find ${\left[4\left(\cos 80^{\circ }+i\sin 80^{\circ }\right)\right]}^6$ in trigonometric form, with the argument on $\left[0^{\circ },360^{\circ }\right)$.