Hi, I'm Tori. Can you help me with this please?
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 isd(t) = 400sec (πt/5). What is the period of d(t)? (Enter only the number.)
+23254 Hi Tori!
Since the function is secant and secant = 1 / cosine, the period of secant will be the same as the period of cosine.
In a function like f(x) = cos( at ) (where t is the variable and a is a constant), the period of that function is found using: period = 2π / a.
In your problem, the value for a = π/5, so the period will be (2π) / (π/5).
2π ÷ (π/5) = 2π · (5/π) = 10 seconds,
which agrees with the problem that says "it completes one rotation every 10 seconds."
+23254 Hi Tori!
Since the function is secant and secant = 1 / cosine, the period of secant will be the same as the period of cosine.
In a function like f(x) = cos( at ) (where t is the variable and a is a constant), the period of that function is found using: period = 2π / a.
In your problem, the value for a = π/5, so the period will be (2π) / (π/5).
2π ÷ (π/5) = 2π · (5/π) = 10 seconds,
which agrees with the problem that says "it completes one rotation every 10 seconds."
