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# sin(2asin(3/4))=?

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sin(2asin(3/4))

Guest Mar 19, 2015

#1
+92256
+10

sin(2asin(3/4))

let      $$\theta=asin(3/4)$$       You should recognise that this is an angle.

$$\\sin(2\theta)=2sin\theta cos\theta\\\\ sin\theta=\frac{3}{4}\\\\ opp=3,\; hyp=4\; adj=\sqrt{16-9}=\sqrt{7}\\\\ cos\theta=\frac{\sqrt7}{4}\\\\ 2sin\theta cos\theta \\\\ =2\times\frac{3}{4}\times\frac{\sqrt7}{4}\\\\ =\frac{6\sqrt7}{16}\\\\\\ sin(2asin(3/4))=\frac{3\sqrt7}{8}\\\\\\$$

Melody  Mar 19, 2015
Sort:

#1
+92256
+10

sin(2asin(3/4))

let      $$\theta=asin(3/4)$$       You should recognise that this is an angle.

$$\\sin(2\theta)=2sin\theta cos\theta\\\\ sin\theta=\frac{3}{4}\\\\ opp=3,\; hyp=4\; adj=\sqrt{16-9}=\sqrt{7}\\\\ cos\theta=\frac{\sqrt7}{4}\\\\ 2sin\theta cos\theta \\\\ =2\times\frac{3}{4}\times\frac{\sqrt7}{4}\\\\ =\frac{6\sqrt7}{16}\\\\\\ sin(2asin(3/4))=\frac{3\sqrt7}{8}\\\\\\$$

Melody  Mar 19, 2015

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