Hey, I'm new to calculus, and I can't figure out this problem.
You start with:
y = TAN (2 SIN x) -pi < x < pi
Since: TAN x = (SIN x / COS x),
you can get
y= SIN (2 SIN x) / COS (2 SIN x)
Then, since the asymptote is where the equation is undefined (or equals infinity), we need to find the value of x which causes the denominator to equal 0.
COS (2 SIN x) = 0
The cosine of +pi/2 is 0, so
2 SIN x = +pi/2
SIN x = +pi/4
x = + SIN^-1 pi/4
The problem is that there are two answers, but I can't figure out how to work out the next one, which the book says is
x = + (pi - SIN^-1[pi/4]
I'd also like a way to type in a pi symbol, if that's possible.