Exam 10: Additional Topics in Trigonometry

Assume that the coordinates of the points $P$ and $e$ are as follows: $P ( - 2,4 ) \quad Q ( 3,6 )$ Draw the vector $\overrightarrow { Q P }$ (using graph paper) and compute its magnitude.

Convert to rectangular form. $r \sin \left( \theta + \frac { \pi } { 4 } \right) = 4$

On a sheet of paper, graph the parametric equation after eliminating the parameter $t$ ( $0 \leq t \leq 2 \pi$ ). Specify the approximate direction on the curve corresponding to increasing values of $t$ . $x = \cos t , y = 2 \sin t$

Carry out the indicated operations. $\left[ \frac { \cos \frac { \pi } { 11 } + i \sin \frac { \pi } { 11 } } { \cos \left( - \frac { \pi } { 11 } \right) + i \sin \left( - \frac { \pi } { 11 } \right) } \right] ^ { 4 }$

Graph the parametric equations using the given range for the parameter $t$ . Begin with the standard viewing rectangle and then make adjustments, as necessary, so that the graph utilizes as much of the viewing screen as possible. For example, in graphing the circle given by $x = \cos t$ and $y = \sin t$ it would be natural to choose a viewing rectangle extending from -1 to 1 in both the $x$ - and $y$ -directions. Graph the parametric equations on a graphing utility. Sketch the result. $x = 5 \cos t$ and $y = 2 \sin t$ , $0 \leq t \leq \frac { \pi } { 2 }$ (one-quarter of an ellipse)