Assume triangle ABC has standard labeling and complete the following.

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

$A, C$, and $c$

For each point given in polar coordinates, state the axis on which the point lies if it is graphed in a rectangular coordinate system. Also, state whether it is on the positive portion or the negative portion of the axis. (For example, $(5,0^{\circ})$ lies on the positive $x$-axis.)

$$(7,360^{\circ})$$

Given u=<-2,5> and v<4,3>, find each vector

v-u

Solve each triangle.

$A=80^{\circ} 40^{\prime}, b=143$ centimeters, $c=89.6$ centimeters

For each rectangular equation, give its equivalent polar equation and sketch its graph.

$$2 x+y=5$$

Vector $\mathbf{v}$ has the given magnitude and direction angle. Write $\mathbf{v}$ in the form $\langle a, b\rangle$.

$$|\mathrm{v}|=69.2, \theta=75^{\circ}$$

Find the cube roots of each complex number: Leave the answers in trigonometric form. Then graph each cube root as a vector in the complex plane.

$$-2 \sqrt{3}+2 i$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator.

$$2(\cos 45^{\circ}+i \sin 45^{\circ})$$

Solve each triangle.

$B=42.88^{\circ}, C=102.40^{\circ}, b=3974$ feet

Vector $\mathbf{v}$ has the given magnitude and direction angle. Write $\mathbf{v}$ in the form $\langle a, b\rangle$.

$|\mathbf{v}|=50, \theta=45^{\circ}$ (give exact values)

Find the modulus $r$ of the number: Do not use a calculator.

$$11-60 i$$

Solve each triangle.

$C=71.83^{\circ}, B=42.57^{\circ}, a=2.614$ centimeters

Find the cube roots of each complex number: Leave the answers in trigonometric form. Then graph each cube root as a vector in the complex plane.

$$2-2 i \sqrt{3}$$

Given u=<-2,5> and v<4,3>, find each vector

u-v