Question

State an equation of a sinusoidal graph with the following properties.

The central axis is at y = 5
Two consecutive minimums are found at (3, −1) and (13, −1
find values for a,b,c and d

Answer 1

<u>The central axis is at y = 5</u>

y = sin(x)+5

<u>Two consecutive minima are found at (3, −1) and (13, −1)</u>
So, the period is 10, the amplitude is 5+1=6, and the shift is 3. cos has max at x=0, but we have a minimum, so

y = -6cos(π/5 (x-3))+5

see the graph at

http://www.wolframalpha.com/input/?i=plot+-6cos%28%CF%80%2F5+%28x-3%29%29%2B5,+x%3D0..15

Answer 2

State an equation of a sinusoidal graph with the following properties.

The central axis is at y = 5
Two consecutive minimums are found at (3, −1) and (13, −1)
find values for a,b,c and d