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Math Help - Unit Circle review

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by ugkwan View Post
    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}}

    Hope this will help you.
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  3. #3
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    Quote Originally Posted by ugkwan View Post
    Hi, I'm having a tough time remember why sin(pie/4) = √(2)/2
    It's pi (not pie).
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  4. #4
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    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
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  5. #5
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    Unhappy

    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
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  6. #6
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    Quote Originally Posted by ugkwan View Post
    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}}

    Does this solve your problem??
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