Hi, I'm having a tough time remember why sin(pie/4) = √(2)/2
I'm basing this on the unit circle with a radius of 1.
legend √( # ) is square root
Dear ugkwan,
Please refer to the attached drawing. There you would see that,
AB=BO
Therefore, by the Pythogorian theorem,
$\displaystyle OA=\sqrt{1^2+1^2}=\sqrt{2}$
Hence by the definition of Sine, $\displaystyle Sin\frac{\pi}{4}=\frac{1}{\sqrt{2}}$
Hope this will help you.
Dear ugkwan,
In my post I have considered a circle with a radius of $\displaystyle \sqrt{2}$. Actually you can consider a circle with any radius you like. For example if the radius is a, then then at $\displaystyle B\hat{O}A=\frac{\pi}{4}\Rightarrow{a=\sqrt{2}b}$ (taking AB=OB=b) Now, $\displaystyle Sin\frac{\pi}{4}=\frac{b}{a}=\frac{b}{\sqrt{2}b}=\ frac{1}{\sqrt{2}}$
Does this solve your problem??