Exam 6: Additional Topics In Trigonometery

Perform the operation shown below and leave the result in trigonometric form. $\left[ 3 \left( \cos 100 ^ { \circ } + i \sin 100 ^ { \circ } \right) \right] \left[ 6 \left( \cos 230 ^ { \circ } + i \sin 230 ^ { \circ } \right) \right]$

A gun with a muzzle velocity of 1700 feet per second is fired at an angle of 4° above the horizontal.Find the vertical and horizontal components of the velocity.(Round your answer to one decimal place.) ​

Find the absolute value of the complex number 5 + 3i.

A 475-pound trailer is sitting on an exit ramp inclined at 32° on Highway 35.How much force is required to keep the trailer from rolling back down the exit ramp $\theta$ Round your answer to two decimal places.

Represent the complex number below graphically. $2 \left( \cos 135 ^ { \circ } + i \sin 135 ^ { \circ } \right)$

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. C = 40°, a = $\frac { 2 } { 15 }$ , b = $\frac { 1 } { 5 }$

Multiply the complex numbers below and leave the result in trigonometric form. $\left[ 0.1 \left( \cos 260 ^ { \circ } + i \sin 260 ^ { \circ } \right) \right] \left[ 0.9 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) \right]$

Find the trigonometric form of $- 6 - 6 \sqrt { 3 } i$ .

Find the angle $\theta$ between the vectors. =6-1 =7+2 (Round the answer to 2 decimal places.)

Perform the operation shown below and leave the result in trigonometric form. $\frac { 48 ( \cos 2.5 + i \sin 2.5 ) } { 8 ( \cos 1.3 + i \sin 1.3 ) }$

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. A = 1, b = $\frac { 1 } { 3 }$ , c = $\frac { 3 } { 4 }$

On a map, Orlando is 187 millimeters due south of Niagara Falls, Denver is 282 millimeters from Orlando, and Denver is 244 millimeters from Niagara Falls (see figure).Find the bearing of Denver from Niagara Falls.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ a = 9, b = 5, c = 10

A straight road makes an angle, A, of 11 $^\circ$ with the horizontal.When the angle of elevation, B, of the sun is 52 $^\circ$ , a vertical pole beside the road casts a shadow 6 feet long parallel to the road, see figure.Approximate the length of the pole.Round answer to two decimal places.

Divide the complex numbers below and leave the result in trigonometric form. $\frac { 2 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) } { 9 \left( \cos 190 ^ { \circ } + i \sin 190 ^ { \circ } \right) }$

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 55°43', a = 6.5, and b = 14

Find the trigonometric form of the complex number shown below. -4 + 4 $\sqrt { 3 }$ i

A tractor pulls a log 900 meters, and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is $35 ^ { \circ }$ above the horizontal.Approximate the work done in pulling the log. (Round the answer to two decimal places.)

Select a value for b such that a triangle with A = 59° and a = 14 has only one solution. ​

Find the dot product of u and v. =6-4 =-