Exam 8: Polar Coordinates; Vectors

Plot the point given in polar coordinates. - $\left( - 3 , - \frac { \pi } { 4 } \right)$ A) B) C) D)

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary. - $- 6$

The rectangular coordinates of a point are given. Find polar coordinates for the point. -(100, -30) Round the polar coordinates to two decimal places, with θ in degrees.

Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. - $r \sec \theta = - 6$ A) $( x + 3 ) ^ { 2 } + y ^ { 2 } = 9$ ; circle, radius 3 center $( - 3,0 )$ in rectangular coordinates B) $y = - 6$ ; horizontal line 6 units below the pole C) $x = - 6$ ; vertical line 6 units to the left of the pole D) $x ^ { 2 } + ( y + 3 ) ^ { 2 } = 9$ ; circle, radius 3 center at $( 0 , - 3 )$ in rectangular coordinates

Find the requested vector. -v = -3i - 5j + k Find a vector orthogonal to both v and i + j.

Find the quantity if v = 5i - 7j and w = 3i + 2j. - $\| \mathbf { v } + \mathbf { w } \|$

State whether the vectors are parallel, orthogonal, or neither. - $\mathrm { v } = \mathrm { i } + 5 \mathrm { j } , \quad \mathbf { w } = \mathrm { i } + \mathrm { j }$

Identify and graph the polar equation. - $r = 4 \theta$ A) logarithmic spiral B) logarithmic spiral C) logarithmic spiral D) logarithmic spiral

Graph the polar equation. - $r=\sin \theta \tan \theta$ A) B) C) D)

Match the graph to one of the polar equations. - A) $r \sin \theta = 3$ B) $r = 6 \cos \theta$ C) $r = 6 \sin \theta$ D) $r = 3$

State whether the vectors are parallel, orthogonal, or neither. -v = 4i + j, w = i - 4j

Graph the polar equation. - $r = \frac { 3 } { 1 - \cos \theta }$ A) B) C) D)

Test the equation for symmetry with respect to the given axis, line, or pole. - $r = 4 - 4 \sin \theta ; \text { polar axis }$

Find all the complex roots. Leave your answers in polar form with the argument in degrees. -The complex fifth roots of $- 2 \mathrm { i }$

Write the complex number in rectangular form. - $3 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Match the point in polar coordinates with either A, B, C, or D on the graph. - $\left( 3 , - \frac { 5 \pi } { 3 } \right)$

The letters r and θ represent polar coordinates. Write the equation using rectangular coordinates (x, y). - $\mathrm { r } = 2 ( \sin \theta - \cos \theta )$

Find the angle between v and w. Round your answer to one decimal place, if necessary. -v = -5i + 7j, w = -6i - 4j

Test the equation for symmetry with respect to the given axis, line, or pole. - $r = 3 - 6 \sin \theta \text {; the polar axis }$

Solve the problem. -An SUV weighing 4,400 pounds is parked on a street which has an incline of 15°. Find the force required to keep the SUV from rolling down the hill and the force of the SUV perpendicular to the hill. Round the forces to the Nearest hundredth.