Question

Find the amplitude, phase shift, and period of the function. Give the exact values, not decimal approximations.y= -1+3cos(2x+pi/3)

Answer 1

The parts of a trigonometric function are:

$y=A\sin(Bx+C)+D$

Where:

A= Amplitude

2PI/B= Period

C= Phase

D= Shift

You have:

$y=3\cos(2x+\frac{\pi}{3})-1$

So

Amplitude= 3

Phase= π/3

Shift= -1

And the period:

$P=\frac{2\pi}{B}=\frac{2\pi}{2}=\pi$

The period = pi