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How would you rewrite sin(x-pi/3)?

1 Answer

Hriman · sankarankalyanam

Mar 11, 2018

Using the sin difference identity...see below

$\frac{sin x - \sqrt{3} cos x}{2}$ $color(blue)((sinx-sqrt3cosx)/2$

Explanation:

$sin (θ - α) = sin θ \cdot cos α - cos θ \cdot sin α$ $sin(theta-alpha)= sintheta*cosalpha-costheta*sinalpha$

So in this case:
$sin (x - \frac{π}{3}) = sin x \cdot cos (\frac{π}{3}) - cos x \cdot sin (\frac{π}{3})$ $sin(x-pi/3)= sinx*cos(pi/3)-cosx*sin(pi/3)$

But we can simplify:
$sin x \cdot (\frac{1}{2}) - cos x \cdot (\frac{\sqrt{3}}{2}) =$ $sinx*(1/2)-cosx*(sqrt3/2)=$

$\frac{sin x - \sqrt{3} cos x}{2}$ $(sinx-sqrt3cosx)/2$

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