# Math Help - Unit Circle review

1. ## Unit Circle review

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

2. Originally Posted by ugkwan
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,

$OA=\sqrt{1^2+1^2}=\sqrt{2}$

Hence by the definition of Sine, $Sin\frac{\pi}{4}=\frac{1}{\sqrt{2}}$

3. Originally Posted by ugkwan
Hi, I'm having a tough time remember why sin(pie/4) = √(2)/2
It's pi (not pie).

4. Please explain why is the hypotenuse √(2) while the radius seems to look like 1, ie. when Cos(0)=1

yes you're right about the pi, haha, I guess I was thinking about apple pies looking at the unit circle

5. never mind the last post, the problem is Im blind to the simple answer from over analyzing a false idea I had in my head. eh

6. Originally Posted by ugkwan
Please explain why is the hypotenuse √(2) while the radius seems to look like 1, ie. when Cos(0)=1

yes you're right about the pi, haha, I guess I was thinking about apple pies looking at the unit circle
Dear ugkwan,

In my post I have considered a circle with a radius of $\sqrt{2}$. Actually you can consider a circle with any radius you like. For example if the radius is a, then then at $B\hat{O}A=\frac{\pi}{4}\Rightarrow{a=\sqrt{2}b}$ (taking AB=OB=b) Now, $Sin\frac{\pi}{4}=\frac{b}{a}=\frac{b}{\sqrt{2}b}=\ frac{1}{\sqrt{2}}$