I'm confused... does sin^2 (x)=2sinx

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ishpiro eNotes educator| Certified Educator

No, sin^2 (x) is the square of sin(x), or sin(x) taken to the second power. By definition, this means sin(x) multiplied by itself two times:

`sin^2(x) = sin(x)*sin(x)` . For example, if x = 30 degrees or `pi/6` radians, then

`sin(x) = sin(pi/6) = 1/2` and `sin^2(pi/6) = (1/2)^2 =1/4`

On the other hand, 2sin(x) is simply two times sin(x): 2*sin(x).

`2sin(x) = 2*sin(pi/6) = 2*1/2 = 1` 

`sin^2(x)` and 2sin(x) are also not to be confused with sin(2x), which is the sine of double x:

`sin(2x) = sin(2*pi/6) = sin(pi/3) = sqrt(3)/2` .

The trigonometric identities relating sin(2x), cos(2x), sin(x) and cos(x) include

`sin(2x) = 2sin(x)cos(x)`


`sin^2(x)= (1-cos(2x))/2` .

Hope this helps.

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