Solve the problem using a graphing calculator.
-A Ferris wheel with a radius of 36 feet turns clockwise at the rate of one revolution every 12 sec. The lowest point of the Ferris wheel is 13 feet above ground level at the point $( 0,13 )$ on a rectangular coordinate system. Find parametric equations for the position of a person on the Ferris wheel as a function of time (in seconds) if the Ferris wheel starts $( t = 0 )$ with the person at the point $( 36,49 )$.
A) $x = 36 \cos ( 30 t ) ^ { \circ } \mathrm { ft } , y = 36 \sin ( 30 \mathrm { t } ) ^ { \circ } + 13 \mathrm { ft }$
B) $x = 36 \cos ( 12 t ) ^ { \circ } \mathrm { ft } , y = 36 \sin ( 12 \mathrm { t } ) ^ { \circ } + 13 \mathrm { ft }$
C) $x = 36 \sin ( 30 t ) ^ { \circ } \mathrm { ft } , y = 36 \cos ( 30 t ) ^ { \circ } + 49 \mathrm { ft }$
D) $x = 36 \cos ( 30 t ) ^ { \circ } \mathrm { ft } , y = 36 \sin ( 30 t ) ^ { \circ } + 49 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The Ferris wheel rotates clockwise at the rate of one revolution every 12 sec, so the angular speed is $ \frac { 2 \pi } { 12 } = \frac { \pi } { 6 } $ radians per second. The person starts at the point $( 36,49 )$, so the initial angle is $ \frac { \pi } { 2 } $ radians. Therefore, the parametric equations for the position of the person on the Ferris wheel as a function of time (in seconds) are:$$x = 36 \cos \left( \frac { \pi } { 6 } t + \frac { \pi } { 2 } \right) \mathrm { ft }$$$$y = 36 \sin \left( \frac { \pi } { 6 } t + \frac { \pi } { 2 } \right) + 13 \mathrm { ft }$$Simplifying these equations gives:$$x = 36 \cos \left( 30 t \right) \mathrm { ft }$$$$y = 36 \sin \left( 30 t \right) + 13 \mathrm { ft }$$

Solve the Problem Using a Graphing Calculator (0,13)( 0,13 )(0,13) On a Rectangular Coordinate System

Solve the Problem Using a Graphing Calculator $( 0,13 )$ On a Rectangular Coordinate System