Question

What is the period of the sinusoid given by y= -3 cos (2pi/5x)?

Answer 1

Answer: 5

Work Shown:

y = -3cos(2pi/5x) is in the form y = A*cos(Bx) where |A| is the amplitude and B helps determine the period T. In this case, B = 2pi/5

T = 2pi/B

T = 2pi/(2pi/5) ... replace B with 2pi/5

T = (2pi/1) divided by (2pi/5)

T = (2pi/1) * (5/2pi)

T = 5 ... note how the '2pi' terms canceled out

So the period is 5

This means that every 5 units on the x axis is when the graph repeats itself.