What is the domain of f(x)=sqrt(sin(x))+sqrt(cos(x)) ?

The domain of f(x)=sqrt(sin(x))+sqrt(cos(x)) is 2pin<= x<= pi/2+2pin

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domain of f(x)=sqrt(sin(x))+sqrt(cos(x))

domain

f (x) = sin (x) + cos (x)

2 πn \leq x \leq \frac{π}{2} + 2 πn

Interval Notation

[2 πn, \frac{π}{2} + 2 πn]

Solution steps

Find non-negative values for radicals:

2 πn \leq x \leq \frac{π}{2} + 2 πn

The function domain

2 πn \leq x \leq \frac{π}{2} + 2 πn

What is the domain of f(x)=sqrt(sin(x))+sqrt(cos(x)) ?
The domain of f(x)=sqrt(sin(x))+sqrt(cos(x)) is 2pin<= x<= pi/2+2pin