Which quadrants and axes does #f(x)=sin(sqrtx)# pass through?

1 Answer
Rhys
Oct 29, 2017

First and fourth quadrant

Explanation:

The function is only valid for #x in RR^+#, as the root of a negative is complex, so hence quadrants 2 and 3 can be disregarded.

Hence the function will pass through Quadrans 1 and 4, for example #sin root2 ((pi/2)^2 )# evidently lies in the first quadrant, and #sin root2 (((3pi)/2)^2)# evidenlty lies in the lies in the fourth quadrant.

Passing through the positive x axis.

graph{y=sin(x^(1/2)) [-9.84, 30.16, -10.4, 9.6]}

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