How do you prove $sin (\frac{5 π}{4})$ $sin ((5pi)/4)$ ?

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Answer 1 · 2016-06-25T15:23:18

$sin (\frac{5 π}{4}) = - \frac{\sqrt{2}}{2}$ $sin((5pi)/4)=-sqrt2/2$

$sin (\frac{5 π}{4}) = sin (π + \frac{π}{4})$ $sin((5pi)/4)=sin(pi+pi/4)$

$sin (a + b) = sin a \cdot cos b + cos a \cdot sin b$ $sin(a+b)=sin a*cos b+cos a*sin b$

$sin (π + \frac{π}{4}) = sin π \cdot cos (\frac{π}{4}) + cos π \cdot sin (\frac{π}{4})$ $sin(pi+pi/4)=sin pi*cos (pi/4)+cos pi*sin(pi/4)$

$sin π = 0; cos π = - 1$ $sin pi=0" ; "cos pi=-1$

$sin (\frac{π}{4}) = \frac{\sqrt{2}}{2}; cos (\frac{π}{4}) = \frac{\sqrt{2}}{2}$ $sin(pi/4)=sqrt 2/2" ; "cos (pi/4)=sqrt2/2$

$sin (\frac{5 π}{4}) = 0 \cdot \frac{\sqrt{2}}{2} - 1 \cdot \frac{\sqrt{2}}{2}$ $sin((5pi)/4)=0*sqrt2/2-1*sqrt2/2$

$sin (\frac{5 π}{4}) = - \frac{\sqrt{2}}{2}$ $sin((5pi)/4)=-sqrt2/2$

How do you prove sin(5π4)sin ((5pi)/4)?