Chapter 11

Find a rectangular equation for each curve and graph the curve. $$x=2+\cos t, y=\sin t-1 ; 0 \leq t \leq 2 \pi$$

For each rectangular equation, give its equivalent polar equation and sketch its graph. $$2 x+y=5$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$2\left(\cos 45^{\circ}+i \sin 45^{\circ}\right)$$

Solve triangle. \(B=42.88^{\circ}, C=102.40^{\circ}, b=3974 \mathrm{feet}\)

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

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

Find a rectangular equation for each curve and graph the curve. $$x=-2+\cos t, y=\sin t+1 ; 0 \leq t \leq 2 \pi$$

For each rectangular equation, give its equivalent polar equation and sketch its graph. $$3 x-2 y=6$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$4\left(\cos 60^{\circ}+i \sin 60^{\circ}\right)$$

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The fourth roots of \(16\left(\cos 240^{\circ}+i \sin 240^{\circ}\right)\).

Solve triangle. \(A=18.75^{\circ}, B=51.53^{\circ}, c=2798\) yards

Solve each triangle. \(B=168.2^{\circ}, a=15.1\) centimeters, \(c=19.2\) centimeters

Graph each pair of parametric equations. $$x=\cos ^{3} t, y=\sin ^{3} t ; 0 \leq t \leq 2 \pi$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. 10 cis \(90^{\circ}\)

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The square roots of \(i\).

Solve each triangle. \(a=3.0\) feet, \(b=5.0\) feet, \(c=6.0\) feet

Graph each pair of parametric equations. $$x=\cos ^{5} t, y=\sin ^{5} t ; 0 \leq t \leq 2 \pi$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$8 \text { cis } 270^{\circ}$$

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The square roots of \(-4 i\).

Graph each pair of parametric equations. $$x=4 \cos t, y=4 \sin 2 t ; 0 \leq t \leq 2 \pi$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$4\left(\cos 240^{\circ}+i \sin 240^{\circ}\right)$$

Determine the number of triangles ABC possible with the given parts. \(a=31, b=26, B=48^{\circ}\)

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The cube roots of \(64 i\).

Refer to the guidelines to solve oblique triangles to decide on the procedure to use to solve each triangle. Then solve the triangle. \(a=59.49, B=50^{\circ} 52^{\prime}, C=28^{\circ} 37^{\prime}\)

Graph each pair of parametric equations. $$x=3 \sin 2 t, y=3 \cos t ; 0 \leq t \leq 2 \pi$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$2\left(\cos 330^{\circ}+i \sin 330^{\circ}\right)$$

Determine the number of triangles ABC possible with the given parts. \(a=35, b=30, A=40^{\circ}\)

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The fourth roots of \(-1\).

Graph each cycloid for t in the specified interval. \(x=t-\sin t, y=1-\cos t ;\) for \(t\) in \([0,4 \pi]\)

Graph each polar equation for \(\theta\) in \(\left[0^{\circ}, 360^{\circ}\right)\). In Exercises \(39-48\), identify the rype of polar graph. $$r=2+2 \cos \theta$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$\cos \frac{\pi}{6}+i \sin \frac{\pi}{6}$$

Determine the number of triangles ABC possible with the given parts. \(a=50, b=61, A=58^{\circ}\)

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The fourth roots of 81.

Graph each cycloid for t in the specified interval. $$x=-2 t+2 \sin t, y=-2+2 \cos t ; \text { for } t \text { in }[0,4 \pi]$$

Graph each polar equation for \(\theta\) in \(\left[0^{\circ}, 360^{\circ}\right)\). In Exercises \(39-48\), identify the rype of polar graph. $$=8+6 \cos \theta$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$3\left(\cos \frac{5 \pi}{6}+i \sin \frac{5 \pi}{6}\right)$$

Determine the number of triangles ABC possible with the given parts. \(B=54^{\circ}, c=28, b=23\)

Find all indicated roots and express them in rectangular form. Check your results with a calculator. The square roots of \(-1+i \sqrt{3}\).

Graph each pair of parametric equations for \(0 \leq t \leq 2 \pi\) in the window \([0,6.6]\) by \([0,4.1] .\) Identify the letter of the alphabet that is being graphed. $$\begin{aligned} &x_{1}=1, \quad y_{1}=1+\frac{t}{\pi}\\\ &x_{2}=1+\frac{t}{3 \pi}, \quad y_{2}=2\\\ &x_{3}=1+\frac{t}{2 \pi}, \quad y_{3}=3 \end{aligned}$$

Graph each polar equation for \(\theta\) in \(\left[0^{\circ}, 360^{\circ}\right)\). In Exercises \(39-48\), identify the rype of polar graph. $$r=3+\cos \theta$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$5 \operatorname{cis}\left(-\frac{\pi}{6}\right)$$

Solve triangle. There may be two, one, or no such triangle. $$A=29.7^{\circ}, b=41.5 \text { feet, } a=27.2 \text { feet }$$

Answer each of the following. For the real number \(1,\) find and graph all indicated roots. Give answers in rectangular form. (a) Fourth (b) Sixth

Refer to the guidelines to solve oblique triangles to decide on the procedure to use to solve each triangle. Then solve the triangle. \(a=51.41, b=37.29, c=65.88\)

Graph each pair of parametric equations for \(0 \leq t \leq 2 \pi\) in the window \([0,6.6]\) by \([0,4.1] .\) Identify the letter of the alphabet that is being graphed. $$\begin{aligned} &x_{1}=1, \quad y_{1}=1+\frac{t}{\pi}\\\ &x_{2}=1+\frac{t}{3 \pi}, \quad y_{2}=2\\\ &x_{3}=1+\frac{t}{2 \pi}, \quad y_{3}=3\\\ &x_{4}=1+\frac{t}{2 \pi}, \quad y_{4}=1 \end{aligned}$$

Graph each polar equation for \(\theta\) in \(\left[0^{\circ}, 360^{\circ}\right)\). In Exercises \(39-48\), identify the rype of polar graph. $$r=2-\cos \theta$$

Write each complex number in rectangular form. Give exact values for the real and imaginary parts. Do not use a calculator. $$6 \text { cis } \frac{3 \pi}{4}$$

Solve triangle. There may be two, one, or no such triangle. $$B=48.2^{\circ}, a=890 \text { centimeters, } b=697 \text { centimeters }$$

Answer each of the following. For the complex number \(i,\) find and graph all indicated roots. Give answers in trigonometric form. (a) Square (b) Fourth

Graph each pair of parametric equations for \(0 \leq t \leq 2 \pi\) in the window \([0,6.6]\) by \([0,4.1] .\) Identify the letter of the alphabet that is being graphed. $$\begin{aligned} &x_{1}=1, \quad y_{1}=1+\frac{t}{\pi}\\\ &x_{2}=1+1.3 \sin 0.5 t, \quad y_{2}=2+\cos 0.5 t \end{aligned}$$