91Ó°ÊÓ

Plot the point whose rectangular coondinates are given. Then determine nwo pairs of polar coondinates for the point with \(0^{\circ} \leq \theta<360^{\circ} .\) Do not use a calculator. $$\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$$

Given vectors u and v, find (a) \(2 u\) (b) \(2 u+3 v\) (c) \(v-3 u\) Do not use a calculator. $$\mathbf{u}=\langle- 2,-1\rangle, \mathbf{v}=\langle- 3,2\rangle$$

Find the modulus \(r\) of the number. Do not use a calculator. $$12-5 i$$

Given \(\mathbf{u}=\langle- 2,5\rangle\) and \(\mathbf{v}=\langle 4,3\rangle,\) find each vector. Do not use a calculator. $$\mathbf{u}+\mathbf{v}$$

Plot the point whose rectangular coondinates are given. Then determine nwo pairs of polar coondinates for the point with \(0^{\circ} \leq \theta<360^{\circ} .\) Do not use a calculator. $$(3,0)$$

Graph each pair of parametric equations for \(0 \leq t \leq 2 \pi .\) Describe any differences in the two graphs. (a) \(x=3 \cos t, \quad y=3 \sin t\) (b) \(x=3 \sin t, \quad y=3 \cos t\)

Solve each triangle. \(A B=1240\) feet, \(A C=876\) feet, \(B C=965\) feet

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. $$1+i \sqrt{3}$$

Plot the point whose rectangular coondinates are given. Then determine nwo pairs of polar coondinates for the point with \(0^{\circ} \leq \theta<360^{\circ} .\) Do not use a calculator. $$(-2,0)$$

Graph each pair of parametric equations for \(0 \leq t \leq 2 \pi .\) Describe any differences in the two graphs. (a) \(x=-1+\cos t, \quad y=2+\sin t\) (b) \(x=1+\cos t, \quad y=2+\sin t\)