Exam 6: Applications of Trigonometry

Find the component form and magnitude of the indicated vector. -Given that $\mathrm { P } = ( 8,9 )$ and $\mathrm { Q } = ( 9,16 )$ , find the component form and magnitude of the vector $\overrightarrow { \mathrm { PQ } }$ .

The polar coordinates of point P are given. Find all of its polar coordinates. - $\mathrm { P } = \left( 7.2,31 ^ { \circ } \right)$

Determine two pairs of polar coordinates for the point with 0° ≤θ < 360°. - $( 0 , - \sqrt { 5 } )$

Plot the point with the given polar coordinates. - $\left( 0,2 ^ { \circ } \right)$

Find an equivalent equation in rectangular coordinates. - $r = \frac { 5 } { 1 + \cos \theta }$

The polar coordinates of point P are given. Find all of its polar coordinates. - $\mathrm { P } = ( - 7 , \pi / 5 )$

Use the given graph to find the values of t that produce the graph in the given quadrant. - $x=3-|t|, y=t+2,-6 \leq t \leq 6$ Quadrant IV

Find an equivalent equation in polar coordinates. - $x = 6$

Solve the problem. -Two forces of $478 \mathrm {~N}$ and $266 \mathrm {~N}$ act at a point. The resultant force is $560 \mathrm {~N}$ . Find the angle between the forces.

Choose the graph of the given parametric equations. - $x = 3 t - 2 , y = t ^ { 2 } - 1 , - 4 \leq t \leq 4$

Write the complex number in the form a + bi. - $3 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$

Prove that $\overrightarrow{R S}$ and $\overrightarrow{O P}$ are equivalent by showing that they represent the same vector. -R = (4, 3), S = (13, 11), O = (0, 0), and P = (9, 8)

Prove that $\overrightarrow{R S}$ and $\overrightarrow{O P}$ are equivalent by showing that they represent the same vector. -R = (5, 1), S = (8, 10), O = (0, 0), and P = (3, 10)

Find the parametrization for the curve. -The line through the points $( 4,3 )$ and $( 9 , - 3 )$

Solve the problem. -The locations, given in polar coordinates, of two planes approaching an airport are $\left( \mathrm { x } \mathrm { mi } , 70 ^ { \circ } \right)$ and $\left( 3 \mathrm { x } \mathrm { mi } , 130 ^ { \circ } \right)$ . Find an expression in terms of $x$ for the distance between the two planes.

Choose the graph of the given parametric equations. - $x = t ^ { 2 } , y = \sqrt { t } + 5,0 \leq t \leq 4$

Find an equivalent equation in polar coordinates. - $y = 10$

Find the product or quotient, as indicated. Leave your answer in polar form. -Find the product of $\mathrm { z } _ { 1 }$ and $\mathrm { z } _ { 2 }$ . $z _ { 1 } = 8 \left( \cos \frac { 4 \pi } { 7 } + i \sin \frac { 4 \pi } { 7 } \right) , z _ { 2 } = \frac { 1 } { 5 } \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle 2 , - 6 \rangle , \mathbf { v } = \langle 5 , - 1 \rangle$ . Find $- 3 \mathbf { u } + 4 \mathbf { v }$ .

Find a· b. - $\mathbf { a } = \langle 3,10 \rangle , \mathbf { b } = \langle 2 , - 3 \rangle$