What is the domain and range for sqrt(sin(x))?

Question

assume you don't know the shape of the graph, without the use of scientific calc and graphic calc. Please give a good explanation.

Answer 1

Since the range of sin(x) is [-1,1], and the square root function can only take positive numbers, [0,1] will be the domain of your function. The range of this function will also be [0,1].

Answer 2

domain of sqrt (X) is X greater than or equal to zero

in your case sin(x) must be greater or equal than zero - this is true in first and second quadrant - for x between 0 and pi (including 0 and pi)

so your domain are all x between 0 and pi or any even multiples of pi added to 0 and pi (example - x between 2pi and 3pi is also in the domain)


range of sin x when x is in I or II quadrant is between 0 and 1

square root will still be in [0,1]

Answer 3

domain = input values

range = output values

domain of x is [0, pi] , [2pi, 3pi], etc and
[-2pi, pi}, [-4pi,-3pi], etc

range of y is [0,1]