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:

`(9\pi)/(4)-(\pi)/(4)=(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=(1)/(2)(3-(-11))=(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-(\pi)/(4))-4`