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Magazine Problem 1
Fill in the blank to correctly complete each sentence. For the plane curve defined by $$ x=t^{2}+1, y=2 t+3, \quad \text { for } t \text { in }[-4,4] $$, the ordered pair that corresponds to \(t=-3\) is__________.
Problem 1
Find each power. Write the answer in rectangular form. Do not use a calculator. $$\left[3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right]^{3}$$
Problem 1
Consider case and determine whether the law of sines should be used to solve the triangle. Two angles and the side included between them are known.
Problem 2
Fill in the blank to correctly complete each sentence. For the plane curve defined by \(x=-3 t+6, y=t^{2}-3, \quad\) for \(t\) in \([-5,5]\),the ordered pair that corresponds to \(t=4\) is __________.
Problem 2
Find each power. Write the answer in rectangular form. Do not use a calculator. $$\left[2\left(\cos 135^{\circ}+i \sin 135^{\circ}\right)\right]^{4}$$
Problem 2
Consider case and determine whether the law of sines should be used to solve the triangle. Two angles and a side opposite them are known.
Problem 3
Fill in the blank to correctly complete each sentence. For the plane curve defined by $$ x=\cos t, y=2 \sin t, \quad \text { for } t \text { in }[0,2 \pi] $$,the ordered pair that corresponds to \(t=\frac{\pi}{3}\) is __________.
Problem 3
Find each power. Write the answer in rectangular form. Do not use a calculator. $$\left(\cos \frac{\pi}{4}+i \sin \frac{\pi}{4}\right)^{8}$$
Problem 4
Find each power. Write the answer in rectangular form. Do not use a calculator. $$\left(\cos \frac{\pi}{5}+i \sin \frac{\pi}{5}\right)^{5}$$
Problem 4
Fill in the blank to correctly complete each sentence. For the plane curve defined by $$ x=-\sin t, y=-2 \cos t, \quad \text { for } t \text { in }[0,2 \pi] $$,the ordered pair that corresponds to \(t=\frac{\pi}{6}\) is__________.
