Question

How do you graph `y = cos(90-A)` as sinA?

Answer 1

Just graphing it. `cos(90 - A) = sin(A)`

Explanation:

There are many ways to go around and show this, the easiest is simply plugging the 5 main values and show that it matches (even though this isn't a proof it's enough to understand)

`cos(90 - 0) = cos(90) = 0 = sin(0)`
`cos(90 - 30) = cos(60) = 1/2 = sin(30)`
`cos(90 - 45) = cos(45) = sqrt2/2 = sin(45)`
`cos(90 - 60) = cos(30) = sqrt3/2 = sin(60)`
`cos(90 - 90) = cos(0) = 1 = sin(90)`
`cos(90 - 180) = cos(-90) = cos(90) = 0 = sin(180)`

We can proof this though, by using the property
`cos(a - b) = cos(a)cos(b) + sin(a)sin(b)`

So

`cos(90 - x) = cos(90)cos(x) + sin(90)sin(x)`

As we've seen on the list above, `cos(90) = 0` and `sin(90) = 1`, thus:

`cos(90 - x) = 0cos(x) + 1sin(x)`
`cos(90 - x) = sin(x)`