## anonymous one year ago simplfy sin(arccos0 + arccos1/2)

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1. Loser66

cos (pi/2) =?

2. Flvs.net

Still need help?

3. anonymous

simplify [0, 180º] sin(arccos 0 + arccos 1/2) .. arccos 0=90º arccos 1/2=60º .. sin(arccos 0 + arccos 1/2) sin(90º+ 60º) =sin 150º =1/2

4. anonymous

did tht help?

5. anonymous

To approach it from a slightly different direction: Let $$x=\arccos0$$ (so that $$\cos x=0$$) and $$y=\arccos\dfrac{1}{2}$$ (so that $$\cos y=\dfrac{1}{2}$$). \begin{align*}\sin(x+y)&=\sin x\cos y+\cos x\sin y\\[1ex] &=\frac{1}{2}\sin x \end{align*} Since $$\cos x=0$$, we have that $$x=\dfrac{k\pi}{2}$$ for nonzero integer $$k$$. Keeping in mind that $$0\le\arccos z\le\pi$$, we omit all values of $$k$$ except $$k=1$$, so $$x=\dfrac{\pi}{2}$$. Finally, what's $$\dfrac{1}{2}\sin\dfrac{\pi}{2}$$?