Exam 6: Additional Topics In Trigonometery

The baseball player in center field is playing approximately 310 feet from the television camera that is behind home plate.A batter hits a fly ball that goes to the wall 400 feet from the camera (see figure).The camera turns 10° to follow the play.Approximately how far does the center fielder have to run to make the catch? ​ ​

Find the standard form of the complex number shown below.Round answers to two decimal places. $2 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right)$

Sketch the graph of all complex numbers z satisfying the given condition. $| z | = 7$

Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 60°.

The vector $\mathbf { u } = \langle 3800,5400 \rangle$ gives the number of units of two models of laptops produced by a company.The vector $\mathbf { v } = \langle 1350,1000 \rangle$ gives the prices (in dollars) of the two models of laptops, respectively.Identify the vector operation used to increase revenue by 3.5%.

Find a unit vector in the direction of $\mathbf { u } = 4 \mathbf { i } - 2 \mathbf { j }$ .

Perform the operation shown below and leave the result in trigonometric form. $\left[ 4 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \right] \left[ 3 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right) \right]$

Given $\mathbf { u } = 5 \mathbf { i } - 3 \mathbf { j }$ and $\mathbf { v } = \mathbf { i } + 2 \mathbf { j }$ , determine $9 \mathbf { u } - 3 \mathbf { v }$ .

Find the standard form of the complex number $5 \left( \cos \frac { 5 \pi } { 12 } + i \sin \frac { 5 \pi } { 12 } \right)$ .Round values to the nearest hundredth.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 29°, b = 14, c = 29 ​

Find values for b such that the triangle has one solution. A = 74°, a = 17

Find a unit vector in the direction of $\mathbf { w } = \langle - 4 , - 6 \rangle$ .

Find all solutions to the following equation. $x ^ { 3 } + 729 = 0$

Find the angle between the vectors u and v if $\mathbf { u } = \langle 3 , - 3 \rangle$ , and $\mathbf { v } = \langle 1 , - 1 \rangle$ Round your answer to two decimal places.

Find u - v. $\mathbf { u } = \mathbf { i } + \mathbf { j } , \mathbf { v } = 2 \mathbf { i } - 3 \mathbf { j }$

Find the angle $\theta$ between the vectors. =\langle4,0\rangle =\langle0,-3\rangle (Round the answer to 1 decimal place.)

Divide the complex numbers below and leave the result in trigonometric form. $\frac { 10 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) } { 7 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) }$

Find the projection of u onto v if , $\mathbf { u } = \langle - 5 , - 4 \rangle$ , $\mathbf { v } = \langle 2 , - 5 \rangle$ .

Find the component form of vector v.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 140°, b = 8, c = 9 ​