Exam 6: Applications of Trigonometry

Choose the graph of the given parametric equations. - $x=\sqrt{t}, y=3 t+2,0 \leq t \leq 4$ .

Use the dot product to find $|\mathbf{v}|$ - $\mathbf { v } = \langle 3,8 \rangle$

Find the product or quotient, as indicated. Leave your answer in polar form. -Find the product of $\mathrm { z } _ { 1 }$ and $\mathrm { z } _ { 2 }$ . $\mathrm { z } _ { 1 } = 3 \left[ \cos \left( - 40 ^ { \circ } \right) + \mathrm { i } \sin \left( - 40 ^ { \circ } \right) \right] , \mathrm { z } _ { 2 } = 44 \left( \cos 180 ^ { \circ } + \mathrm { i } \sin 180 ^ { \circ } \right)$

Find a· b. - $\mathbf { a } = 4 \mathbf { i } + 6 \mathbf { j } , \quad \mathbf { b } = - 5 \mathbf { i } - 0.5 \mathbf { j }$

Solve the problem. -An airplane is flying on a bearing of $310 ^ { \circ }$ at $560 \mathrm { mph }$ . Find the component form of the velocity of the airplane. Round your answer to the nearest hundredth.

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 7 , - 3 \rangle , \mathbf { v } = \langle 1,9 \rangle$ . Find $\mathbf { v } - \mathbf { u }$ .

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

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 9 , - 4 \rangle , \mathbf { v } = \langle - 7 , - 1 \rangle$ . Find $\mathbf { u } + \mathbf { v }$ .

Find the component form and magnitude of the indicated vector. -Given that $\mathrm { P } = ( - 9,6 )$ and $\mathrm { Q } = ( - 17,11 )$ , find the component form and magnitude of the vector $3 \overrightarrow { \mathrm { PQ } }$ .

Use the given graph to find the values of t that produce the graph in the given quadrant. - $x=2-|t|, y=t-1,-6 \leq t \leq 6$ Quadrant III

Plot the point with the given polar coordinates. - $\left(3,-150^{\circ}\right)$

Find the product or quotient. Write the answer in standard form. - $\frac { 7 - 8 i } { 7 + 4 i }$

Find the component form of the vector v. -

Eliminate the parameter. - $x = \sqrt { t } , y = 2 t + 5$

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

Prove that $\overrightarrow{R S}$ and $\overrightarrow{O P}$ are equivalent by showing that they represent the same vector. -R = (6, 3), S = (7, 5), O = (9, 8), and P = (11, 10)

Solve the problem using a graphing calculator. -Anne can sprint at a rate of $22 \mathrm { ft } / \mathrm { sec }$ . Carol can sprint at $27 \mathrm { ft } / \mathrm { sec }$ . Carol gives Anne a $10 - \mathrm { ft }$ head start. The parametric equations below can be used to model a race. =22t, =3 =27t-10, =5 Find a viewing window to simulate a 200 -yd dash. Graph simultaneously. Who is ahead after 8 seconds and by how much?

Find the component form and magnitude of the indicated vector. -Given that $P = ( - 4,8 ) , Q = ( - 3,13 ) , R = ( 3 , - 5 )$ , and $S = ( 7,0 )$ , find the component form and magnitude of the vector $\overrightarrow { \mathrm { PQ } } + 2 \overrightarrow { \mathrm { RS } }$ .

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 5 , - 8 \rangle , \mathbf { v } = \langle - 6 , - 7 \rangle$ . Find $\mathbf { u } - \mathbf { v }$ .

Find the component form of the vector v. -