How do you know if #y=sin^2(x)# is an even or odd function?

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Answer 1 · 2018-03-23T07:40:41

#y = sin^2 x " is an even function"#

#color(brown)("What is an even function?")#
1. #color(green)("An even function is symmetric about the y-axis."#
2. #color(purple)(f(-x) = f(x)#

#color(orange)("What is an odd function?"#
1. #color(blue)("An odd function is symmetric about the origin".#
2. #color(red)(f(-x) = -f(x)#

Given : # y = sin^2x#

#f(x) = sin^2 x#

#f(-x) = sin^2 (-x) = (sin(-x))^2 = (-sin x)^2 = sin^2 x = f(x)#

Hence it is an even function.

graph{(sin x)^2 [-10.54, 9.46, -5.32, 4.68]}