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How do you find the value of #sin^2(225^circ)#?

Answer 1

Charles Autterson

#sin^2 225^o=1/2#

As #sin(180+A)=-sinA#

#sin225^o=sin(180^o+45^o)=-sin45^o#

but #sin45^o=1/sqrt2# and hence #sin225^o=-1/sqrt2#

Hence, #sin^2 225^o=(-1/sqrt2)^2=1/2#

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Answer 2

Grace Ashcraft

To find the value of sin^2(225°), you first convert 225° to radians because trigonometric functions typically work with radians. Since 1 full rotation in degrees equals 2π radians, you can convert 225° to radians by multiplying by (π/180):

225° * (π/180) = (5π/4) radians

Now, sin^2(225°) is equivalent to sin^2((5π/4)). Using the identity sin^2(x) = (sin(x))^2, you simply need to square the sine of (5π/4):

sin(5π/4) = -√2/2

Now, square this value:

(sin(5π/4))^2 = (-√2/2)^2 = 2/4 = 1/2

So, the value of sin^2(225°) is 1/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.