Circular Motion problem

Question

A point starts at the location (2.5,0) and moves counter-clockwise along a circular path with a radius of 2.5 units that is centered at the origin of an x-y plane. An angle with its vertex at the circle's center measures θθ radians and subtends the path the point travels. Let x represent the point's x-coordinate

A. Write an expression (in terms of θ) to represent the point's distance to the right of the center of the circular path in radii

B. Write a formula that expresses x in terms of θ.

C.If the angle has swept out 3.9 radians since the point started moving, what is the point's x-coordinate

Answer 1

A) The distance to the right is a weird expression. It's either distance in the horizontal direction from the center or it's displacement to the right (that allows values that are <0 to the left) or it is unstated that we are limited to the first quadrant. If the first is meant, then the distance away from the center horizontally is |rcosθ|.

B) x = rcosθ = 2.5cosθ

C) plug in and make sure your calculator is in radians. (3.9 radians is obviously greater than π/2, so we are not limited to the first quadrant.

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