The range of y=2/3 sin x for π<x<3π/2 is option b which is -2/3<y<0.
What is range?
Range is basically a limit under which the value of variable, function lies.
It is also known as codomain of the function.
How to find range?
We have been given function as y=2/3 sin x and we have to find the range of the function for π<x<3π/2.
We have to just put x=π and x=3π/2 in the function and then we will be able to write range of function because we know that when the upper limit and lower limit of domain is entered in the function then we will get the upper limit and lower limit of function.
at x=π, y=2/3 sin π
y=2/3*0
y=0
at x=3π/2
y=2/3 sin (3π/2)
y=2/3 sin(π+π/2)
y=-2/3 sin π/2
y=-2/3
Range will be (-2/3,0).
Hence the range of y=2/3 sin x for π<x<3π/2 is option b which is -2/3<y<0.
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