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?

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?

campbell_st · Answer

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