A skier skis along a circular ski trail that has a radius of 1.3 km. The skier starts at the East side of the ski trail and travels in the CW (clockwise) direction. Let
θ
represent the varying number of radians the skier has swept out in the CW direction.
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).
1.3cos(theta)
Correct
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).
1.3sin(theta)
Incorrect
Ok what was wrong with the last one.
Well, you see, when a skier skis along a circular trail, the distance to the North of the center actually depends on the cosine function, not the sine function. The cosine function represents the skier's distance to the East, while the sine function represents the skier's distance to the North. So, the correct expression to represent the skier's distance to the North of the center of the ski trail is 1.3sin(theta).
I apologize for the confusion. The expression to represent the skier's distance to the North of the center of the ski trail is indeed 1.3sin(theta), so you had the correct answer.
The expression that represents the skier's distance to the North of the center of the ski trail is actually incorrect. The correct expression is 1.3sin(θ), as you initially stated.
The reason it is correct is because when dealing with circular motion, the sine function represents the vertical component or the distance in the North direction, while the cosine function represents the horizontal component or the distance in the East direction.
In this case, since the skier starts at the East side and travels in the clockwise direction, the varying number of radians swept out in the CW direction, represented by θ, affects the skier's distance in the North direction. Therefore, the correct expression is 1.3sin(θ).