Suppose joe is skiing around a circular track with a 4 km ra

Suppose joe is skiing around a circular track with a 4 km radius. After leaving the starting point, joe travels counter-clockwise for 2.7 km.

What are the x and y coordinates of joes location on this circle of radius 4 km?

Solution : radius r = 4 km, arc length = 2.7 km.

Thus angle (theta) = arc / radius

=2.7/4=0.675 rad.

We know that x coordinate = r cos (theta)

=4 cos (0.675)=3.122.

We also know that y coordinate =r sin(theta)

=4sin(0.675)=2.499.