Domain of f(x) = sqrt(1-sin(x)): Understanding and Calculating

[unf0r5ak3n]

Homework Statement

let f(x) = sqrt(1-sin(x))

Homework Equations

What is the domain of f?
What is the domain of f'(x)?

The Attempt at a Solution

I understand that the domain of f is all real numbers not including every increment of 90 degrees, but I am not sure how to state that.
I also found that f'(x) = (1/2 -sin(x))(-cos(x)) I am not sure if that's correct though

 

[micromass]

A point is not in the domain if it does not have a function value. The only possible situation that $$f(x)=\sqrt{1-sin(x)}$$ does not exist, is when you take the root of a negative number. So you will have to search for what x we have that 1-sin(x)<0.

 

[cloud360]

go on google and type

wolfrom alpha

look at the graphs and try understand

 

[hunt_mat]

Micromass is spot on here, for what values of x satisfy $$\sin x\leqslant 1$$? Do you know the graph of $$\sin x$$?

 

[unf0r5ak3n]

so the domain is all real numbers except when sin(x)<1?

 

[micromass]

Yes! But can you say explicitly when sin(x)<1?

 

[hunt_mat]

No that's not what we're saying the domain if all numbers which satisfy sin(x)<1, not the other way around.

 

[unf0r5ak3n]

thats where i got lost