Expert: Steve Holleran - 5/7/2008

Question
For f(x) = 2 sin(2x+Pi/4)

The amplitude= ?
The period=?
the phase shift-?

Answer
Hi Cameron,

Okay, we've got f(x) = 2 sin(2x + pi/4)

The amplitude is the absolute value of the multiplier in the front of the sine function, so ampl = 2.

The period is always 2pi divided by the coefficient of x; here, the coefficient is 2, so the period = 2pi/2 = pi.

To get the phase shift, set the argument, 2x + pi/4, = 0 and solve for x:

   2x + pi/4 = 0 --> 2x = -pi/4 --> x = -pi/8  .  This is a shift to the left by pi/8 units.

Hope this helps out.

Steve