Find the value of $sin(2x)$ and $cos(2x)$ on the unit circle
Answer 1
Benjamin Clark
To find the value of $\sin(2x)$ and $\cos(2x)$ on the unit circle, we can utilize the double-angle formulas:
$ \sin(2x) = 2\sin(x)\cos(x) $
$ \cos(2x) = \cos^2(x) – \sin^2(x) $
Given a point on the unit circle (a, b) where $a = \cos(x)$ and $b = \sin(x)$, we can substitute:
$ \sin(2x) = 2ab $
$ \cos(2x) = a^2 – b^2 $
Answer 2
Isabella Walker
Using the double-angle identities, we find:
$ sin(2x) = 2sin(x)cos(x) $
$ cos(2x) = cos^2(x) – sin^2(x) $
For any point on the unit circle (a, b) where $a = cos(x)$ and $b = sin(x)$, we get:
$ sin(2x) = 2ab $
$ cos(2x) = a^2 – b^2 $
Answer 3
Michael Moore
Use the double-angle formulas:
$ sin(2x) = 2sin(x)cos(x) $
$ cos(2x) = cos^2(x) – sin^2(x) $
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