Exam 9: Applications of Trigonometry

Find the product. Write the product in rectangular form, using exact values. - $\left[ 4 \left( \cos 120 ^ { \circ } + \mathrm { i } \sin 120 ^ { \circ } \right) \right] \left[ 5 \left( \cos 120 ^ { \circ } + \mathrm { i } \sin 120 ^ { \circ } \right) \right]$

Answer the question. -If $\mathrm { n }$ is an odd number, then which of the following statements is true?

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in $\left[ 0,360 ^ { \circ } \right]$ - $\langle \sqrt { 21 } , - 1 \rangle$

Find the component form of the indicated vector. -Let $\mathbf { u } = \langle - 7,6 \rangle , \mathbf { v } = \langle - 7 , - 4 \rangle$ . Find $\mathbf { u } - \mathbf { v }$ .

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. -A stained glass window is composed of 20 triangular sections, each with sides 4,7 , and 8 in. Find the total area of the window (to the nearest square inch).

Find the missing parts of the triangle. - =33 =18.76 =16.15 If necessary, round side lengths to the nearest hundredth.

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 2 - \cos \theta$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $- 3 \sqrt { 3 } + 3 i$

Find the dot product for the pair of vectors. -9, -13, 9, 10

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. Round to one decimal place. -Two forces, of $32.9$ and $43.1 \mathrm { lb }$ , forming an angle of $46.3 ^ { \circ }$ , act at a point in the plane. Find the magnitude of the resultant force.

Graph the complex number. - $-5+i$

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. -Two ships leave a harbor together traveling on courses that have an angle of $128 ^ { \circ }$ between them. If they each travel 543 miles, how far apart are they (to the nearest mile)?

Write the complex number in trigonometric form r(c $r ( \cos \theta + i \sin \theta )$ ), with $\theta$ in the interval [0 $\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $- 2 \mathrm { i }$

Find all specified roots. -Fifth roots of 1.

Use the figure to find the specified vector. -Find - $\mathbf { a }$ .

Answer the question. -On which line do the square roots of $- \mathrm { i }$ lie?

Considering the given value of t, choose the ordered pair that lies on the graph of the given pair of parametric equations. - $x = t ^ { 2 } - 8 , y = t ^ { 2 } + 2 ; t = 2$

Write the complex number in trigonometric form r(c $r ( \cos \theta + i \sin \theta )$ ), with $\theta$ in the interval [0 $\left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $9 + 9 i$

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. -The sides of a parallelogram are $14 \mathrm { ft }$ and $16 \mathrm { ft }$ . One angle is $41 ^ { \circ }$ while another angle is $139 ^ { \circ }$ . Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 10 \operatorname { cis } 332 ^ { \circ } } { 5 \operatorname { cis } 62 ^ { \circ } }$