Exam 8: Complex Numbers, Polar Equations, and Parametric Equations

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = \sin t , y = \cos t ; t = \frac { 5 \pi } { 6 }$

The graph of a polar equation is given. Select the polar equation for the graph -

Perform the indicated operations. Simplify the answer. - $\sqrt { - 64 } \cdot \sqrt { - 4 }$

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\left[ 5 \operatorname { cis } \frac { 4 \pi } { 9 } \right] ^ { 2 }$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 5 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) } { 4 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }$

Find an equivalent equation in rectangular coordinates. - $\mathrm { r } = 10 \sin \theta$

The graph of a polar equation is given. Select the polar equation for the graph -

Find the product. Write the product in rectangular form, using exact values. - $\left[ 7 \left( \cos 120 ^ { \circ } + \mathrm { i } \sin 120 ^ { \circ } \right) \right] \left[ 2 \left( \cos 90 ^ { \circ } + \mathrm { i } \sin 90 ^ { \circ } \right) \right]$

Solve the quadratic equation and express all nonreal complex solutions in terms of i. - $x ^ { 2 } + 80 = 0$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may - $5 \mathrm { i }$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 20 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) } { 4 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right) }$

The graph of r = a in polar coordinates is an example of the spiral of Archimedes. With your calculator set to radian mode, use the given value of a and interval of to graph the spiral in the window specified. - $a=3,0 \leq \theta \leq 2 \pi,[-20,20] \text { by }[-20,20]$

Solve the problem. -A projectile is fired with an initial velocity of 350 feet per second at an angle of 45° with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the Nearest tenth of a second.)

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = \sin t , y = 3 \cos t$

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = t ^ { 2 } - 6 , y = t ^ { 2 } + 1 ; t = 3$

Find the quotient. Write the answer in standard form. - $\frac { 3 } { 5 \mathrm { i } }$

Find sum of the pair of complex numbers. - $- 7 i , - 9 - 4 i$

Graph the polar equation for in [0°, 360°). - $r = 5 ( \cos \theta + \cos 2 \theta )$

Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve. -

Find all cube roots of the complex number. Leave answers in trigonometric form. --8