trigonometry graphing

Question

Write a cosine function that has a midline of y=2,y=2, an amplitude of 4 and a period of \frac{5\pi}{7}​.



Answer 1

We will start off using the period to find the B value for the equation.

period = 2π/B

5π/7 = 2π/B Cross multiply

14π = 5πB Divide by 5π

14π/5π = 5πB/5π

B=14/5

The rest plug directly in the equation. The amplitude goes in front of the cos, the midline change is added at the end as a vertical shift 2 units up.

y=4cos (14x/5)+2