Assume triangle $ABC$ has standard labeling and complete the below.

Decide whether the law of sines or the law of cosines should be used to begin solving the triangle.

$$b, c, \text{ and } A$$

For the given pair of polar coordinates. Plot the point.

$$\left(2,-45^{\circ}\right)$$

For the vectors $\mathbf{u}=\langle-1,3\rangle$ and $\mathbf{v}=\langle 2,-6\rangle$, find the given.

$$\mathbf{u}+\mathbf{v}$$

Assume triangle $ABC$ has standard labeling and complete the below.

Determine whether SAA, ASA, SSA, SAS, or SSS is given.

$$b, c, \text{ and } A$$

For this plane curve graph the curve

$x=t^2, y=\sqrt{t}$, for $t$ in $[0,4]$

Determine whether the pair of vectors is orthogonal.

$$\langle 1,0\rangle,\langle\sqrt{2}, 0\rangle$$

Find an equivalent equation in polar coordinates.

$$y=x^2$$

Find an equivalent equation in polar coordinates.

$$y=x$$

Determine whether the pair of vectors is orthogonal.

$$\langle 3,4\rangle,\langle 6,8\rangle$$

Find an equivalent equation in rectangular coordinates.

$$r=2$$

Determine whether the pair of vectors is orthogonal.

$$\langle 1,2\rangle,\langle-6,3\rangle$$

Find an equivalent equation in rectangular coordinates.

$$r=\sin \theta+\cos \theta$$

Let $\mathbf{u}=\langle-2,1\rangle, \mathbf{v}=\langle 3,4\rangle$, and $\mathbf{w}=\langle-5,12\rangle$.

Evaluate the expression.

$$u \cdot(3 v)$$

Let $\mathbf{u}=\langle-2,1\rangle, \mathbf{v}=\langle 3,4\rangle$, and $\mathbf{w}=\langle-5,12\rangle$.

Evaluate the expression.

$$u \cdot v-u \cdot w$$