Exam 9: Applications of Trigonometry

Graph the polar equation for $\theta \text { in } \left[ 0 ^ { \circ } , 360 ^ { \circ } \right)$ - $r = 6 + 6 \sin \theta$

Find sum of the pair of complex numbers. --3 + 7i, 9i

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 50 , | \mathbf { w } | = 12 , \theta = 35 ^ { \circ }$

Solve the problem. -If u =-3, 5 and v =4, -2 , evaluate (2u) ·v.

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

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( - 3 \sqrt { 2 } , - 3 \sqrt { 2 } )$

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( - 3,0 )$

Find all cube roots of the complex number. Leave answers in trigonometric form. - $- 6 \sqrt { 3 } - 6 i$

Solve the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. -

Graph the cycloid for t in the indicated interval. - $x = 3 ( t - \sin t ) , y = 3 ( 1 - \cos t ) , 0 \leq t \leq 6 \pi$

Give two parametric representations for the equation of the parabola. - $y = ( x + 1 ) ^ { 2 } + 9$

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal places. - $\left[ 5 \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right) \right] \left[ 4 \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right) \right]$

Determine two pairs of polar coordinates for the point with $0 ^ { \circ } \leq \theta < 360 ^ { \circ }$ - $( 2 \sqrt { 3 } , 6 )$

Sketch the vectors u and w with angle $\theta$ between them and sketch the resultant. - $| \mathbf { u } | = 3 , | \mathbf { w } | = 12 , \theta = 40 ^ { \circ }$

Find a rectangular equation for the plane curve defined by the parametric equations. - $x = t + 4 , y = t ^ { 2 }$

Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form. - $\frac { 9 + 5 i } { 6 - 9 i }$

Provide an appropriate response. -A trigonometry student makes the statement, "If we know any two sides and one angle of a triangle, then the triangle is uniquely determined." Is this a valid statement? Explain, referring to the congruence axioms.

Solve the problem. -A projectile is fired with an initial velocity of 600 feet per second at an angle of 45° with the horizontal. To the nearest 10 feet, find the horizontal distance covered by the projectile.

The graph o $r = a \theta$ in polar coordinates is an example of the spiral of Archimedes. With your calculator set to radian mode, use the given value of a and interval of  to graph the spiral in the window specified. - $a = 2 , - 3 \pi \leq \theta \leq 3 \pi , [ - 20,20 ]$ by $[ - 20,20 ]$

Determine whether the pair of vectors is orthogonal. -3, 6 , -6, 6