# Thread: Find a Trigonometric equation

1. ## Find a Trigonometric equation

Give an equation for a cosine funtion that has a maximum at (pi/4, 8), followed immediately by another maximum at (9pi/4,8), and has a minimum at value of 4.

This is what I did

Amplitude = (8-4)/2
= 2

Vertical shift = 8-2 =6

So far I got this
y = 2cos (x -? )+6

How do I find the phase shift

2. The cosine function normally has consecutive maximums at $x = 0$ and $x = 2\pi$. Your function has consecutive maximums at $x = \frac{\pi}{4}$ and $x = \frac{9\pi}{4}$. This means the period is $\frac{9\pi}{4} - \frac{\pi}{4} = 2\pi$, which is normal for the cosine function. So what is the phase shift when you move $(0, 8)$ to $(\frac{\pi}{4}, 8)$?