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sin v = 0,5

Decide the value of: sin 2v

Guest May 5, 2017
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sin v = 0,5

Decide the value of: sin 2v

 

\(\begin{array}{rcl|rcl|rcl} \sin(2v) &=& 2\cdot \sin(v)\cdot \cos(v) & \cos(v) &=& \sqrt{1-\sin^2(v)} & \sin(v) = \frac12 \\ & & & &=& \sqrt{1-\left(\frac12 \right)^2} \\ & & & &=& \sqrt{1- \frac14} \\ & & & &=& \sqrt{\frac34} \\ & & & &=& \frac{\sqrt{3}}{2} \\ &=& 2\cdot \frac12\cdot \frac{\sqrt{3}}{2} & &=& \frac{\sqrt{3}}{2} \\ &=& \frac{\sqrt{3}}{2} \\ \end{array} \)

 

\(\sin(2v) = \frac{\sqrt{3}}{2}\)

 

laugh

heureka  May 5, 2017

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