Complete the table for the function y=5 sin (3x-180^o) - 2

Question

Amplitude
Period
Phase shift
Equation of the axis
Max/Min

Answer 1

The standard sine function looks like this:

y = Asin[B(x - C)] + D where

A = amplitude

B = 2π/period

C = phase shift (or horizontal shift)

D = vertical shift (in other words y = D is the equation of the midline or principal axis)

So looking at the given equation:

y = 5sin(3x - 180°) - 2

we need to slightly modify it to fit our generic function above, Notice that I must factor out the "B" to get it correct.

so the slightly modified function is y = 5sin[3(x - 60°)] - 2

Now we can see that:

A = 5

B = 3 meaning that 3 = 2π/period or the period = 2π/3

C = 60° (to the right) or +60°

D = -2 so y = -2 is the equation of the principal axis (usually called the midline)

The min and max are calculated as D + A and D - A so that would be -2 + 5 (or 3) and -2 - 5 (or -7)