Exam 6: Additional Topics in Trigonometry

In the figure below, $a = 9 , b = 11$ , and $c = 12$ . Use this information to solve the parallelogram for $\theta$ . The diagonals of the parallelogram are represented by $c$ and $d$ . Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. $- 3 - 3 i$

Find the component form of vector $\mathbf { v }$ with initial point $( - 5,1 )$ and terminal point $( - 3 , - 2 )$ .

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $B = 75 ^ { \circ } 22 ^ { \prime } , a = 11$ , and $c = 14$

Find the component form of vector $\mathbf { v }$ .

Find the angle between the vectors $\mathbf { u }$ and $\mathbf { v }$ . $\mathbf { u } = \cos \left( \frac { \pi } { 3 } \right) \mathbf { i } + \sin \left( \frac { \pi } { 3 } \right) \mathbf { j } , \quad \mathbf { v } = \cos \left( \frac { 5 \pi } { 4 } \right) \mathbf { i } + \sin \left( \frac { 5 \pi } { 4 } \right) \mathbf { j }$

Plot the following complex number. $3 i$

Given $\mathbf { u } = \langle - 3,7 \rangle$ and $\mathbf { v } = \langle 1 , - 5 \rangle$ , find $\mathbf { u } \cdot \mathbf { v }$ .

Given $a = 13 , b = 11$ , and $c = 6$ , use Heron's Area Formula to find the area of triangle $A B C$ . Round answer to two decimal places.

A plane flies 450 kilometers with a bearing of $319 ^ { \circ }$ from City A to City B (see figure below). The plane then flies 730 kilometers from City B to City C, which is directly west of City A. Find the bearing of the flight from City B to City C. Round your answer to two decimals.

Find the vector $\mathbf { v }$ that has a magnitude of 4 and is in the same direction as $\mathbf { u }$ , where $\mathbf { u } = \langle - 5 , - 3 \rangle$ .

Find the standard form of the complex number shown below. Round answers to two decimal places. $6 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right)$

Given $a = 7 , b = 5$ , and $c = 8$ , use the Law of Cosines to solve the triangle for the value of $B$ . Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. $- 3 i$

A force of 50 pounds is exerted along a rope attached to a crate at an angle of $30 ^ { \circ }$ above the horizontal. The crate is moved 43 feet. How much work has been accomplished? Round answer to one decimal place.

A 400 -pound trailer is sitting on an exit ramp inclined at $31 ^ { \circ }$ on Highway 35 . How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

Find the trigonometric form of the complex number shown below. $- 7 i$

A force of 45 pounds is exerted along a rope attached to a crate at an angle of $30 ^ { \circ }$ above the horizontal. The crate is moved 50 feet. How much work has been accomplished? Round answer to one decimal place.

Determine the area of a triangle having the following measurements. Round your answer to two decimal places. $C = 59 ^ { \circ } 24 ^ { \prime } , a = 6$ , and $b = 14.5$

Given $A = 16 ^ { \circ } , b = 12$ , and $a = 10$ , use the Law of Sines to solve the triangle (if possible) for the value of $c$ . If two solutions exist, find both. Round answer to two decimal places.