Chapter 11

Find the modulus \(r\) of the number. Do not use a calculator. $$6+8 i$$

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. $$\left(\frac{\sqrt{3}}{2}, \frac{3}{2}\right)$$

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. $$-64$$

Solve triangle. \(C=74.08^{\circ}, B=69.38^{\circ}, c=45.38\) meters

Given vectors u and v, find (a) \(2 u\) (b) \(2 u+3 v\) (c) \(v-3 u\) Do not use a calculator. $$\mathbf{u}=\langle- 1,2\rangle, \mathbf{v}=\langle 3,0\rangle$$

Solve each triangle. \(a=42.9\) meters, \(b=37.6\) meters, \(c=62.7\) meters

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

Find the modulus \(r\) of the number. Do not use a calculator. $$3-4 i$$

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. $$\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$$

Solve triangle. \(A=87.2^{\circ}, b=75.9\) yards, \(C=74.3^{\circ}\)

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

Solve each triangle. \(a=189\) yards, \(b=214\) yards, \(c=325\) yards

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

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

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. $$(3,0)$$

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

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

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

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) \(x=1+\cos t, \quad y=2+\sin t\)

Find the modulus \(r\) of the number. Do not use a calculator. $$-24+7 i$$

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. $$(-2,0)$$

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

Solve triangle. \(B=20^{\circ} 50^{\prime}, C=103^{\circ} 10^{\prime}, b=132 \mathrm{feet}\)

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

Solve each triangle. \(A B=298\) meters, \(A C=421\) meters, \(B C=324\) meters

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

For each rectangular equation, give its equivalent polar equation and sketch its graph. $$x-y=4$$

Find the modulus \(r\) of the number. Do not use a calculator. $$-6$$

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

Solve triangle. \(A=35.3^{\circ}, B=52.8^{\circ}, b=675 \mathrm{feet}\)

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

Find a rectangular equation for each curve and graph the curve. $$x=\tan t, y=\cot t ; \text { for } t \text { in }\left(0, \frac{\pi}{2}\right)$$

Find the modulus \(r\) of the number. Do not use a calculator. $$15 i$$

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

Solve triangle. \(A=68.41^{\circ}, B=54.23^{\circ}, a=12.75 \mathrm{feet}\)

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

Solve each triangle. \(C=72^{\circ} 40^{\prime}, a=327\) feet, \(b=251\) feet

Find a rectangular equation for each curve and graph the curve. $$x=2+\sin t, y=1+\cos t ; \text { for } t \text { in }[0,2 \pi]$$

For each rectangular equation, give its equivalent polar equation and sketch its graph. $$x^{2}+y^{2}=16$$

Find the modulus \(r\) of the number. Do not use a calculator. $$2-3 i$$

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The square roots of \(4\left(\cos 120^{\circ}+i \sin 120^{\circ}\right)\).

Solve triangle. \(A=39.70^{\circ}, C=30.35^{\circ}, b=39.74\) meters

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

Find a rectangular equation for each curve and graph the curve. $$x=1+2 \sin t, y=2+3 \cos t ; \text { for } t \text { in }[0,2 \pi]$$

For each rectangular equation, give its equivalent polar equation and sketch its graph. $$x^{2}+y^{2}=9$$

Find the modulus \(r\) of the number. Do not use a calculator. $$-5+6 i$$

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The cube roots of \(27\left(\cos 180^{\circ}+i \sin 180^{\circ}\right)\).

Solve triangle. \(C=71.83^{\circ}, B=42.57^{\circ}, a=2.614\) centimeters

Given \(\mathbf{u}=\langle- 2,5\rangle\) and \(\mathbf{v}=\langle 4,3\rangle,\) find each vector. Do not use a calculator. $$3 u+6 v$$

Solve each triangle. \(C=59.70^{\circ}, a=3.725\) miles, \(b=4.698\) miles