The rotating light on a lighthouse is 400 feet from a cliff. It completes one rotation every 10 seconds. The equation representing the distance, d, in feet that the center of the circle of light is from the lighthouse is d(t) = 400sec (πt/5). What is the period of d(t)? (Enter only the number.)
for y = cos kt
the period would be 2π/k
since the period of sec is the same as the period of sin
period = 2π/(π/5)
= 2π(5/π)
= 10
Didn't it tell you that at the beginning ?
To find the period of the equation d(t), we need to identify the period within the equation. The period represents the time it takes for the function to repeat its pattern.
In the given equation, d(t) = 400sec(πt/5), the period is determined by the coefficient of 't' within the trigonometric function. In this case, the coefficient is π/5.
The period, T, is calculated using the formula T = (2π)/|coefficient of t|.
Substituting the coefficient from the given equation, we have:
T = (2π)/|(π/5)|
Simplifying further:
T = (2π)/(π/5)
T = (2π) * (5/π)
T = 10
Therefore, the period of d(t) is 10 seconds.