Exam 8: Applications of Trigonometry

Solve. -A complex number $\mathrm { z }$ does not belong to the Mandelbrot set if any of the complex numbers in the sequence $z , z ^ { 2 } + z , \left( z ^ { 2 } + z \right) ^ { 2 } + z , \left[ \left( z ^ { 2 } + z \right) ^ { 2 } + z \right] ^ { 2 } + z , \ldots$ has modulus exceeding 2 . Does $z = 2$ belong to the Mandelbrot set?

Find the missing parts of the triangle. - =94. =15.2 =38.3 If necessary, round angles and side lengths to the nearest tenth.

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. -

Determine the number of triangles ABC possible with the given parts. - $\mathrm { a } = 24 , \mathrm {~b} = 20 , \mathrm {~A} = 40 ^ { \circ }$

Write the complex number in trigonometric form $r ( \cos \theta + i \sin \theta )$ with θ in the interval [0°, 360°). - $- \sqrt { 7 } - \mathrm { i } \sqrt { 7 }$

The rectangular coordinates of a point are given. Express the point in polar coordinates with r ≥ 0 and 0° ≤ θ < 360°. - $( 3,3 )$

Find the product. Write the product in rectangular form, using exact values. - $\left[ 4 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) \right] \left[ 6 \left( \cos 330 ^ { \circ } + i \sin 330 ^ { \circ } \right) \right]$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 2 \sqrt { 3 } + 2 i } { \sqrt { 3 } - i }$

Solve the problem. -If $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle 7,6 \rangle$ , and $\mathbf { w } = \langle - 11,2 \rangle$ , evaluate $\mathbf { u } \cdot \mathbf { v } + \mathbf { u } \cdot \mathbf { w }$ .

Find sum of the pair of complex numbers. - $12 - 11 \mathrm { i } , 5 + 3 \mathrm { i }$

Determine whether the pair of vectors is orthogonal. - $\langle - 1 , \sqrt { 3 } \rangle , \langle - 2 \sqrt { 3 } , - 3 \rangle$

Sketch the vectors u and w with angle θ between them and sketch the resultant. - $| \mathbf { u } | = 2.85 , | \mathbf { w } | = 2.85 , \theta = 90 ^ { \circ }$

Find an equivalent equation in rectangular coordinates. - $\mathrm { r } - 5 \sin \theta = 5 \cos \theta$

Provide an appropriate response. -True or false? The parametric equations $x = 2 \tan t , y = 3 \sec t$ will graph a parabola.

Assume a triangle ABC has standard labeling. Determine whether SAA, ASA, SSA, SAS, or SSS is given. Then whether the law of sines or the law of cosines should be used to begin solving the triangle. - $a , b$ , and $B$

Write the vector in the form ai + bj. - $\langle - 9,3 \rangle$

Give the rectangular coordinates for the point. - $\left( - 5 , \frac { 3 \pi } { 2 } \right)$

Find the angle between the pair of vectors to the nearest tenth of a degree. - $3 \mathbf { i } - 5 \mathbf { j } , 4 \mathbf { i } - 9 \mathbf { j }$

Sketch the vectors u and w with angle θ between them and sketch the resultant. - $| \mathbf { u } | = 8 , | \mathbf { w } | = 16 , \theta = 15 ^ { \circ }$

Write the complex number in rectangular form. - $3 \left( \cos 9 ^ { \circ } + i \sin 9 ^ { \circ } \right)$