Exam 6: Applications of Trigonometry

Draw the graph of $r=a+a \cos \theta \text { where } a \geq 1 \text {. }$ (Make sure you label the scale on your graph.)

Let A=(2,5), B=(-3,6) . Express the vector determined by $\overrightarrow{A B}$ as a linear combination of $\mathbf{i}=\langle 1,0\rangle \text { and } \mathbf{j}=\langle 0,1\rangle$

Write the complex number $2 \sqrt{3}\left(\cos \frac{2 \pi}{3}+i \sin \frac{2 \pi}{3}\right)$ in standard form.

In Problems $15-16$ , assume that $w=5\left(\cos \frac{\pi}{12}+i \sin \frac{\pi}{}\right)$ is one of the six roots of a complex number $z$ . $\text { Determine } z \text {. Express your answer in standard form. }$

What is the parameterization of the line through the points (5,-4) and (2,6) ?

Eliminate the parameter from the curve C defined by the parametric equations $x(t)=t^{2}+2 \text { and } y(t)=5-t$

A golf ball is hit with an initial velocity of 150 ft/sec at an angle of 29° from the horizontal. How long is the ball in the air?

An airplane is flying on a bearing of $265^{\circ}$ at 420 mph. A wind is blowing with a bearing of $210^{\circ}$ at 30 mph. Find the actual speed and direction of the plane and explain how you arrived at your answer.

Let A=(5,2), B=(-2,4) . Express the vector determined by $\overrightarrow{A B}$ as a linear combination of $\mathbf{i}=\langle 1,0\rangle \text { and } \mathbf{j}=\langle 0,1\rangle$

Find the polar equation that corresponds to the graph below.

Draw the graph of $r^{2}=9 \sin 2 \theta$

What is the vector projection of $\mathbf{u}=\langle 8,-2\rangle$ onto $\mathbf{v}=\langle 4,-4\rangle ?$