Question

A skier skis along a circular ski trail that has a radius of 1.25 km. The skier starts at the East side of the ski trail and travels in the CCW direction. Let θ represent the radian measure of the angle the skier has swept out.Write an expression (in terms of θ) to represent the skier's distance to the East of the center of the ski trail (in km).   Write an expression (in terms of θ) to represent the skier's distance to the North of the center of the ski trail (in km).

Answer 1

Point a. To solve the exercise you can first make a drawing to understand the situation.

Since the skier starts from the East of the center of the ski trail and reaches the East of the center of the ski trail again, then finding the distance that the skier travels is equivalent to finding the perimeter of the ski trail.

The formula to find the perimeter of a circle is

`\begin{gathered} P=2\pi r \\ \text{ Where r is the radius of the circle and} \\ 2\pi\text{ is the angle} \\ \end{gathered}`

So, in this case, you have