Exam 6: Applications of Trigonometry

Find the magnitude and direction angle for the following vector. Give the direction angle as an angle in [0°, 360°) rounded to the nearest tenth. - $\langle 11,7 \rangle$

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. - $[ - 5,5 ]$ by $[ - 5,5 ]$

Find a· b. - $\mathbf { a } = \langle 3,7 \rangle , \mathbf { b } = \langle 3,4 \rangle$

Find the product or quotient, as indicated. Leave your answer in polar form. -Find the quotient. $\frac { 7 \left( \cos 35 ^ { \circ } + i \sin 35 ^ { \circ } \right) } { 3 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right) }$

Find the rectangular coordinates of the point with the given polar coordinates. - $( - 4 , - \pi / 3 )$

Find the parametrization for the curve. -The circle with center $( 7,9 )$ and radius 2

Solve the problem. -Find the work done by a force $F$ of 20 pounds acting in the direction $\langle 1,5 \rangle$ in moving an object 4 feet from $( 0,0 )$ to $( 4,0 )$ .

Choose the graph of the given parametric equations. - $x = 3 \sin 3 t , y = 2 \cos t$

Analyze the graph of the given polar curve. Include the following information: If possible, describe the shape of the graph (circle, rose curve, limacon, etc.), and state the domain, range, and maximum r-value of the graph. State whether the graph is continuous and whether it is bounded. Describe any symmetry that the graph has. Give the equations of any asymptotes or state that the graph has no asymptotes. - $r ^ { 2 } = 16 \cos 2 \theta , 0 \leq \theta \leq 2 \pi$

Solve the problem using a graphing calculator. -Determine which will travel farther: baseball $x$ hit 123 feet per second at an angle of $35 ^ { \circ }$ relative to level ground or baseball y hit 118 feet per second at an angle of $30 ^ { \circ }$ .

Draw a graph of the rose curve. - $r = 2 \sin 3 \theta , 0 \leq \theta \leq 2 \pi$

Analyze the graph of the given polar curve. Include the following information: If possible, describe the shape of the graph (circle, rose curve, limacon, etc.), and state the domain, range, and maximum r-value of the graph. State whether the graph is continuous and whether it is bounded. Describe any symmetry that the graph has. Give the equations of any asymptotes or state that the graph has no asymptotes. - $\mathrm { r } = 7 - 3 \cos \theta$

Prove that $\overrightarrow{R S}$ and $\overrightarrow{O P}$ are equivalent by showing that they represent the same vector. -R = (4, 5), S = (8, 8), O = (5, 6), and P = (9, 9)

Find a· b. - $a = \langle - 4 , - 1 \rangle , \quad b = \langle 5.5,3 \rangle$

Find an equivalent equation in rectangular coordinates. - $r = \frac { 5 } { 2 \sin \theta + 6 \cos \theta }$

Find an equivalent equation in rectangular coordinates. - $r - 6 \sin \theta = 4 \cos \theta$

Find an equivalent equation in rectangular coordinates. - $\mathbf { r } = \cos \theta$

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. - $r = 3 \cos 3 \theta$

Find an equivalent equation in rectangular coordinates. - $\mathrm { r } ( 1 - 2 \cos \theta ) = 1$

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. - $r = 3 + 3 \sin \theta$