Thread: Sinusoidal function help

A small windmill has its center 10 meters above the ground and blades 4 meters in length. In a steady wind, a point P at the tip of one blade makes a rotation in 24 seconds.

If the rotation begins at the highest possible point, determine a function that gives the height of point P above the ground at a time T

Originally Posted by imakeitrain

A small windmill has its center 10 meters above the ground and blades 4 meters in length. In a steady wind, a point P at the tip of one blade makes a rotation in 24 seconds.

If the rotation begins at the highest possible point, determine a function that gives the height of point P above the ground at a time T

1. Draw a sketch.

2. According to my sketch the point P has the coordinates P(x, 10+y).

3. Since the argument of the sine function is an angle measured against(?) the horizontal axis the argument here must be when you calculate the x-coordinate.

4. According to the text of the question a blade of the mill makes a full turn in 24 s. If T is measured in seconds the angle is calculated by:



5. Since the argument of the cosine function is an angle measured against(?) the horizontal axis the argument here must be when you calculate the y-coordinate.

6. Therefore you have:



7. Since you are only interested in the height above ground you'll get:

Nicely done, earboth!