What is the period of the function? Give an exact value.

Question

Below is the graph of a trigonometric function. It intersects its midline at (−3.5,−0.8)left parenthesis, minus, 3, point, 5, comma, minus, 0, point, 8, right parenthesis and it has a maximum point at (4.1,0.7)left parenthesis, 4, point, 1, comma, 0, point, 7, right parenthesis.

What is the period of the function? Give an exact value.

Answer 1

The distance between the midline intersection and the first maximum for a sine wave is 1/4 of the period. In this case that is 4(4.1 - (-3.5)) = 4•7.6 = 30.4.

As an FYI, the amplitude is the "y" difference between the midline and the maximum so 0.7 - (-0.8) = 1.5 so the function would be:

y = 1.5sin(5π/76(x + 3.5)) - 0.8 with a curve like this: