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.

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

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

$$\left(-2,135^{\circ}\right)$$

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

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

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

For the below equation, find an equivalent equation in rectangular coordinates and graph.

$$r=2 \sec \theta$$

Find the quotient and write it in rectangular form. First, convert the numerator and the denominator to trigonometric form.

$$\frac{2 \sqrt{6}-2 i \sqrt{2}}{\sqrt{2}-i \sqrt{6}}$$

Given $\mathbf{u}=\langle-2,5\rangle$ and $\mathbf{v}=\langle 4,3\rangle$, find the given.

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

Solve the problem.

The layout for a child's playhouse has the dimensions . Find $x$.

Perform the operation. Write answers in rectangular form.

$$\left(\cos 100^{\circ}+i \sin 100^{\circ}\right)^6$$

A rocket tracking facility has two radar stations $T_1$ and $T_2$, placed $1.73 \mathrm{~km}$ apart, that lock onto the rocket and continuously transmit the angles of elevation to a computer. Find the distance to the rocket from $T_1$ at the moment when the angles of elevation are $28.1^{\circ}$ and $79.5^{\circ}$, as shown in the given figure.

Show that if z is an nth root of 1, then so is $\frac{1}{z}$.

Find the quotient and write it in rectangular form. First, convert the numerator and the denominator to trigonometric form.

$$\frac{1}{2-2 i}$$

For the below equation, find an equivalent equation in rectangular coordinates and graph.

$$r=\frac{3}{4 \cos \theta-\sin \theta}$$

Perform the operation. Write answers in rectangular form.

$$(2-2 i)^5$$

True or false: Some real numbers have three real cube roots.