Describe the method you would use to solve the following equation for $0^{\circ} \leq x<360^{\circ}$.

$\sin ^{2} x=\sin x$.

Determine whether each statement is true or false. If false, replace the underlined term or expression to make the statement true. If $\mathbf{V}$ is a unit vector in the same direction as $\mathbf{U},$ then $\underline{\mathbf{V}=\frac{|\mathbf{U}|}{\mathbf{U}}}.$

Solve the following equations given that $0^{\circ} \leq \theta<360^{\circ}:$ $\cos 2 \theta=-\frac{1}{2}$

In unit-vector notation, if $\vec{a}=$ $(4.0 \mathrm{~m}) \hat{\mathrm{i}}+(3.0 \mathrm{~m}) \hat{\mathrm{j}}$ and $\vec{b}=(-13.0 \mathrm{~m}) \hat{\mathrm{i}}+(7.0 \mathrm{~m}) \hat{\mathrm{j}}$ ? What is the magnitude of $\vec{a}+\vec{b}$ ?

Suppose f is differentiable at (3,4). Assume u, v, and w are unit vectors, $\mathbf{v}=-\mathbf{u}, \mathbf{w} \cdot \mathbf{\nabla} f(\mathbf{3}, 4)=\mathbf{0}$, and $D_{\mathbf{u}} f(\mathbf{3}, 4)=\mathbf{7}$. Find $D_{v} f(3,4)$ and $D_{w} f(3,4)$.

An electron's position is given by $\vec{r}=3.00 t \hat{\mathrm{i}}-4.00 t^2 \hat{\mathrm{j}}+$ $2.00 \hat{\mathrm{k}}$, with $t$ in seconds and $\vec{r}$ in meters. In unit-vector notation, what is the electron's velocity $\vec{v}(t)$ ?

Let

$$\mathbf{u}=\left[\begin{array}{l} 1 \\ 5 \end{array}\right] \quad \mathbf{v}=\left[\begin{array}{l} 2 \\ 1 \end{array}\right]$$

Find a unit vector in the direction of u.

Given $\vec{c}=4 \vec{i}+7 \vec{j}$ and $\vec{d}=5 \vec{i}+2 \vec{j}$.

Find a unit vector, $\vec{u}$, in the direction of $\vec{c}$. Use the result to find a vector 7 units long in the direction of $\vec{c}$.

Convert to polar coordinates with $r \geq 0$ and $0^{\circ} \leq \theta<360^{\circ}$.

$$(-2 \sqrt{3}, 2)$$

Convert to polar coordinates with $r \geq 0$ and $0^{\circ} \leq \theta<360^{\circ}$.

$$(2,-2 \sqrt{3})$$

Solve the following equations given that $0^{\circ} \leq \theta<360^{\circ}:$ $-2+\sqrt{3} \sec \theta=0$

Use the indicated method to solve the system.

$$\text {Cramer's Rule: }\left\{\begin{array}{l} 2 x-7 y=7 \\ 3 x+7 y=13 \end{array}\right.$$

In unit-vector notation, what is the sum $\vec{a}+\vec{b}$ if $\vec{a}=$ $(4.0 \mathrm{~m}) \hat{\mathrm{i}}+(3.0 \mathrm{~m}) \hat{\mathrm{j}}$ and $\vec{b}=(-13.0 \mathrm{~m}) \hat{\mathrm{i}}+(7.0 \mathrm{~m}) \hat{\mathrm{j}}$ ?

Use Cramer's Rule to solve each system of equations.

$$\left\{ \begin{array} { r r } { 3 x + y - z = 14 } \\ { x + 3 y - z = 16 } \\ { x + y - 3 z = - 10 } \end{array} \right.$$