What is the exact period of 5*cos(5x - pi/2) ?

Question

I need the answer in radians.

Answer 1

Period = 2π / 5

Answer 2

The period of the cosine is 2pi.

Now in an expression such as the one given, it is the 5x term that determines the period. The constant term -pi/2 is just an offset that slides the curve along the x-axis.

Take the cosine to go from 0 to 2pi. You want the first term to do this also. so:

5x = 0 and x = 0

5x = 2pi and x = (2/5)pi

So the period of the function is (2/5)pi

Answer 3

The period is 2PI over the coefficient of x for a cosine function.

Period = 2PI / 5