Question

I need some help solving this problem it’s from my ACT prep guide This is trigonometry subject

Answer 1

From the graph we notice that the period of the function is 2pi, this comes from the fact that the first maximum is at pi/4 and the second at 9pi/4, then the period is:

$\frac{9\pi}{4}-\frac{\pi}{4}=\frac{8\pi}{4}=2\pi$

And hence the period of the function is 2pi.

Also, from the graph we notice that the amplitude is 7 this can be seen as follows: the amplitude is half the distance from the minimum to the maximum, then we have:

$A=\frac{1}{2}(3-(-11))=\frac{1}{2}(14)=7$

The vertical shift of the graph is -4 and the horizontal shift is pi/4 to the right; hence we have that the function is:

$f(x)=7\cos (x-\frac{\pi}{4})-4$