This is a pretty basic question however I simply wanted clarification. I know that sin(theta) is opposite/hypotenuse regarding right triangles. But what would certainly sin(2theta) be? would it be (opposite/hypotenuse) * 2? My problem here is my sin(theta) is x/3. But would sin(2theta) it is in (2x/3)?




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The number $\sin(2\theta)$ is the sine of double the edge $\theta$. It is almost never same to $2\sin(\theta)$.

But there is an important "double-angle" identification $$\sin(2\theta)=2\sin(\theta)\cos(\theta)\tag1$$ the you can use in her problem. If you understand that $\sin(\theta)=\fracx3$, all you need to do to discover $\sin(2\theta)$ is to discover $\cos(\theta)$ and also then usage the identity (1).


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$\sin 2\theta \not=2\sin \theta$, however 4\sin 2\theta = 2\sin \theta \cos \theta$

As we know, $\cos2\theta \not= 2\cos \theta$, $$\cos2\theta=\sin^2 \theta-\cos^2\theta=2\cos^2\theta-1=1-2\sin^2\theta.$$


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