Question

for a medal: how do i find the domain of cosx / (2+sinx)?
i set the denominator equal to 0 and got sinx= -2. then i did sin inverse and got an error. what is the correct way to solve this?

Answer 1

well thats he correct method,

the problem is value of sin(x) is always between -1 and 1

that is the range of the function is

\[-1\le \sin(x) \le 1\]

so

you can't find an angle that will result in

sin(x) = -2

because the angle doesn't exist

so the domain is all real x.

in other words, you can put any value of x in the denominator and you'll get a positive value..

I've attached a graph of the curve... the horizontal scale is in radians

hope it helps