Chapter 11

Find a rectangular equation for each curve and describe the curve. $$x=\cot t, y=\csc t ; \text { for } t \text { in }(0, \pi)$$

Plot each point, given its polar coordinates. Give two other pairs of polar coordinates for each point. Do not use a calculator. $$\left(-1,-120^{\circ}\right)$$

Graph each complex number as a vector in the complex plane. Do not use a calculator. $$2$$

Find each power. Write the answer in rectangular form. Do not use a calculator. $$\left(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} i\right)^{8}$$

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=t+2, y=t^{2} ; \text { for } t \text { in }[-1,1]$$

Plot each point, given its polar coordinates. Give two other pairs of polar coordinates for each point. Do not use a calculator. $$\left(3, \frac{5 \pi}{3}\right)$$

Answer each of the following. The modulus of a complex number represents the __________ of the vector representing it in the complex plane.

Find each power. Write the answer in rectangular form. Do not use a calculator. $$(1-i)^{6}$$

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=2 t, y=t+1 ; \text { for } t \text { in }[-2,3]$$

Plot each point, given its polar coordinates. Give two other pairs of polar coordinates for each point. Do not use a calculator. $$\left(4, \frac{3 \pi}{2}\right)$$

Answer each of the following. What is the geometric interpretation of the argument of a complex number?

Find each power. Write the answer in rectangular form. Do not use a calculator. $$(-1+i)^{7}$$

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=\sqrt{t}, y=3 t-4 ; \text { for } t \text { in }[0,4]$$

Answer each of the following. What must be true for a complex number to also be a real number?

Find each power. Write the answer in rectangular form. Do not use a calculator. $$(-2-2 i)^{5}$$

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=t^{2}, y=\sqrt{t} ; \text { for } t \text { in }[0,4]$$

Plot each point, given its polar coordinates. Give two other pairs of polar coordinates for each point. Do not use a calculator. $$(-1,2 \pi)$$

Answer each of the following. If a real number is graphed in the complex plane, on what axis does the vector lie?

Find each power. Write the answer in rectangular form. Do not use a calculator. $$(-3-3 i)^{3}$$

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=t^{3}+1, y=t^{3}-1 ; \text { for } t \text { in }(-\infty, \infty)$$

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. $$(-1,1)$$

Find the sum of each pair of complex numbers. Express your answer in rectangular form. Do not use a calculator. $$4-3 i,-1+2 i$$

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. $$1$$

Solve each triangle. \(C=28.3^{\circ}, b=5.71\) inches, \(a=4.21\) inches

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=2 t-1, y=t^{2}+2 ; \text { for } t \text { in }(-\infty, \infty)$$

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. $$(1,1)$$

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. $$i$$

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=t+2, y=\frac{1}{t+2} ; \text { for } t \neq-2$$

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. $$(0,3)$$

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. $$8\left(\cos 60^{\circ}+i \sin 60^{\circ}\right)$$

Solve each triangle. \(C=45.6^{\circ}, b=8.94\) meters, \(a=7.23\) meters

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=t-3, y=\frac{2}{t-3} ; \text { for } t \neq 3$$

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. $$(0,-3)$$

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. $$27\left(\cos 300^{\circ}+i \sin 300^{\circ}\right)$$

Solve each triangle. \(A=67.3^{\circ}, b=37.9\) kilometers, \(c=40.8\) kilometers

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=t+2, y=t-4 ; \text { for } t \text { in }(-\infty, \infty)$$

Find the sum of each pair of complex numbers. Express your answer in rectangular form. Do not use a calculator. $$2+6 i,-2 i$$

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. $$(\sqrt{2}, \sqrt{2})$$

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. $$-8 i$$

Solve triangle. \(A=37^{\circ}, C=95^{\circ}, c=18\) meters

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

Solve each triangle. \(a=9.3\) inches, \(b=5.7\) inches, \(c=8.2\) inches

For each plane curve, (a) graph the curve, and (b) find a rectangular equation for the curve. $$x=t^{2}+2, y=t^{2}-4 ; \text { for } t \text { in }(-\infty, \infty)$$

Find the sum of each pair of complex numbers. Express your answer in rectangular form. Do not use a calculator. $$7+6 i, 3 i$$

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

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. $$27 i$$

Solve triangle. \(B=52^{\circ}, C=29^{\circ}, a=43\) centimeters

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

Solve each triangle. \(a=28\) feet, \(b=47\) feet, \(c=58\) feet

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) \(x=3 \cos 2 t, \quad y=3 \sin 2 t\)