91Ó°ÊÓ

Solve triangle. There may be two, one, or no such triangle. $$C=68.5^{\circ}, c=258 \text { centimeters, } b=386 \text { centimeters }$$

The screen shown to the right is an example of a Lissajous figure. Lissajous figures occur in electronics and may be used to find the frequency of an unknown voltage. Graph each Lissajous figure for \(0 \leq t \leq 6.5\) in the window \([-6.6,6.6]\) by \([-4.1,4.1]\). $$x=2 \cos t, y=3 \sin 2 t$$

Solve triangle. There may be two, one, or no such triangle. $$A=38^{\circ} 40^{\prime}, a=9.72 \text { kilometers, } b=11.8 \text { kilometers }$$

Find all complex solutions for each equation. Leave your answers in trigonometric form. $$x^{3}-8=0$$

Write each complex number in trigonometric form, where \(r\) is exact and \(0 \leq \theta<2 \pi\) $$4 \sqrt{3}+4 i$$

Write each vector in the form ai \(+\) bj. Round a and b to the nearest hundredth, if necessary. Direction angle \(115^{\circ},\) magnitude 0.6

Answer each question.How do you graph \((r, \theta)\) by hand if \(r<0 ?\).

Answer each question.For \(r>0,\) the points \((r, \theta)\) and \(\left(-r, \theta+180^{\circ}\right)\) have the same graph. Why this is so?

Find all complex solutions for each equation. Leave your answers in trigonometric form. $$x^{5}+1=0$$

The screen shown to the right is an example of a Lissajous figure. Lissajous figures occur in electronics and may be used to find the frequency of an unknown voltage. Graph each Lissajous figure for \(0 \leq t \leq 6.5\) in the window \([-6.6,6.6]\) by \([-4.1,4.1]\). (GRAPH CANNOT COPY) $$x=2 \sin 2 t, y=3 \cos 3 t$$