Exam 6: Additional Topics In Trigonometery

Use the vectors $\mathbf { u } = \langle 3,5 \rangle$ , $\mathbf { v } = \langle - 2,2 \rangle$ , and $\mathbf { w } = \langle 5 , - 3 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $( 3 \mathbf { w } \cdot \mathbf { v } ) \mathbf { u }$

Use the Law of Sines to solve (if possible) the triangle.Round your answers to two decimal places. ​ A = 76°, a = 7, b = 5 ​

Three forces with magnitudes of 74 pounds, 98 pounds, and 105 pounds act on an object at angles 170°, 220°, and 330°, respectively, with the positive x-axis.Find the magnitude and direction of the resultant force.Round answers to two decimal places.

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​ A = 170, B = 20°, C = 15° ​

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129 $^\circ$ , b = 9 and c = 7.

Find the trigonometric form of $- 9 + 9 i$ .

Find the trigonometric form of $- 18 \sqrt { 3 } - 18$ .

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector. Initial Point Terminal Point (-9,9) (10,-10)

Use vectors to find the measure of the angle at vertex B of triangle ABC, when $A = ( 5,1 )$ , $B = ( - 5,1 )$ , and $C = ( - 3 , - 5 )$ .Round answer to two decimal places.

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 84°38', a = 7, and c = 8

Perform the indicated operation using the standard form. $5 i ( 1 - \sqrt { 2 } i )$

Perform the operation and leave the result in trigonometric form. $\frac { 5 \left( \cos 4.5 ^ { \circ } + i \sin 4.5 ^ { \circ } \right) } { 4 \left( \cos 2.4 ^ { \circ } + i \sin 2.4 ^ { \circ } \right) }$

The vector $\mathbf { u } = \langle 2500,3000 \rangle$ gives the number of units of two models of laptops produced by a company.The vector $\mathbf { v } = \langle 2000,1000 \rangle$ gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%.

The vector $\mathbf { u } = \langle 2700,4700 \rangle$ gives the number of units of two models of laptops produced by a company.The vector $\mathbf { v } = \langle 1200,900 \rangle$ gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 6%.

Write the complex number in trigonometric form.

Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 30°.

Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. ​ A = 18, b = 20, C = 65° ​

In the figure, $\alpha$ and $\beta$ are positive angles. A = 9, b = 18 Write $\alpha$ as a function of $\beta$ .

Find a unit vector in the direction of the given vector. $\mathbf { v } = 2 \mathbf { i } + 2 \mathbf { j }$

Represent the complex number graphically, and find the trigonometric form of the number. 5 + 5i