Question

Not sure how to do this question
Create a table of values for the following and show your work:
f(x) = -2 cos(Ɵ – π/2) for -4π ≤Ɵ ≤ 4π

Answer 1

Whenever you need to construct a table of values, always start with your parent equation: f(Ɵ) = cos(Ɵ). In this case our domain is -4π ≤ Ɵ ≤ 4π, so let's choose our test values to be -2π, -3π/2, -π, -π/2, 0. I'm going to do the negatives because the corresponding positive values are exactly the same. I'm also stopping at -2π because remember the function repeats every 2π radians (e.g. f(-π) = f(-3π), etc). We use these values because they're easy (and you should know them!). You can use more or less test values depending on what you need. If you plug in these values into your parent equation, you get the following:

Ɵ | f(Ɵ)
-2π | 1
-3π/2 | 0
-π | -1
-π/2 | 0
0 | 1

Now look at the transformations in your new function and apply them to this table of values. You need to ADD π/2 to all x-values, and MULTIPLY all y-values by -2. So:

Ɵ + π/2 | -2 f(Ɵ)
-3/2π | -2
-π | 0
-π/2 | 2
0 | 0
π/2 | -2

And there is a (partial) table of values for your new function! Does that make sense?

Answer 2

Perfect, Thank you!