A plane is flying at $500 \mathrm { mph }$ on a bearing of $x ^ { \circ }$ where $x$ is greater than 90 . Give an expression for the component form of the velocity of the plane.
A) $\left( 500 \cos ( 450 - x ) ^ { \circ } , 500 \sin ( 450 - x ) ^ { \circ } \right)$
B) $\left( 500 \sin ( 450 - x ) ^ { \circ } , 500 \cos ( 450 - x ) ^ { \circ } \right)$
C) $\left( 500 \cos x ^ { \circ } , 500 \sin x ^ { \circ } \right)$
D) $\left( 500 \cos ( 90 + x ) ^ { \circ } , 500 \sin ( 90 + x ) ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

The component form of the velocity of the plane can be expressed using trigonometric functions of the angle with respect to the positive x-axis. Since the bearing is given as $x^\circ$ where $x > 90$, it means the plane is flying in the second quadrant. The correct transformation to align with the coordinate system's positive x-axis involves subtracting the angle from 450 degrees, which correctly adjusts for the bearing's orientation. This results in the components $\left( 500 \cos ( 450 - x ) ^ { \circ } , 500 \sin ( 450 - x ) ^ { \circ } \right)$.

A Plane Is Flying At 500mph500 \mathrm { mph }500mph On a Bearing Of

A Plane Is Flying At $500 \mathrm { mph }$ On a Bearing Of