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Consider angles A and B in standard position, in the xy-plane. The measure of an
Consider angles A and B in standard position, in the xy-plane. The measure of angle A is ?4 radians, and the measure of angle B is 3?4 radians. The terminal rays of both angles intersect a circle centered at the origin with radius of 5 units. What is the distance between these two points of intersection: the circle and terminal ray of angle A and the circle and terminal ray of angle B? Explain.
A: 7.071 units; the points of intersection are reflections of each other over the x-axis, therefore we can use sin(?4)−5sin(3?4) to calculate the vertical displacement.
B: 7.071 units; the points of intersection are reflections of each other over the y-axis, therefore we can use
5cos(?4)−5cos(3?4) to calculate the horizontal displacement.
C: 3.536 units; the points of intersection are reflections of each other over the y-axis, therefore we can use sin(?4)+5sin(3?4) to calculate the horizontal displacement.
D: 3.536 units; the points of intersection are reflections of each other over the x-axis, therefore we can use cos(?4)+5cos(3?4) to calculate the vertical displacement.
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