How do you find the exact value of $sin (\frac{5 π}{3})$ $sin ((5pi)/3)$ ?

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Answer 1 · 2016-07-31T09:22:06

$sin (\frac{5 π}{3}) = - \frac{\sqrt{3}}{2}$ $sin ( (5pi)/3)=-sqrt(3)/2$

$sin (\frac{5 π}{3}) = sin (2 π - \frac{π}{3})$ $sin((5pi)/3)=sin(2pi-pi/3)$

$sin (2 π - \frac{π}{3}) = - sin (\frac{π}{3})$ $sin(2pi-pi/3)=-sin(pi/3)$

Period of sin is 2pi and 2pi-pi/3 is in the 4th quadrant.
so sin is negative.

$sin (\frac{5 π}{3}) = sin (2 π - \frac{π}{3}) = - sin (\frac{π}{3})$ $sin ((5pi)/3)=sin(2pi-pi/3)=-sin(pi/3)$

$sin (\frac{π}{3}) = \frac{\sqrt{3}}{2}$ $sin(pi/3)=sqrt(3)/2$

so $sin (\frac{5 π}{3}) = - \frac{\sqrt{3}}{2}$ $sin ( (5pi)/3)=-sqrt(3)/2$

How do you find the exact value of sin(5π3)sin ((5pi)/3)?