Posted by **ashely** on Thursday, December 9, 2010 at 3:24am.

find the exact value of cos 3.14/8

- trig -
**MathMate**, Thursday, December 9, 2010 at 7:56am
Since 3.14 is an approximation to π,

I suppose you mean finding the *exact* value of cos(π/8).

Use the half angle formulae:

cos²(x/2)=(1+cos(x))/2...(1)

sin²(x/2)=(1-cos(x))/2...(2)

The second formula is not required for this problem, but I suggest you memorize both of them, because they will be very useful in your academic life.

Start from known values,

cos(π/2)=0

cos²(π/4)=(1+0)/2

cos(π/4)=(√2)/2

Apply the formula one more time to get cos(π/8):

cos²(π/8)=(1+(√2)/2))/2

cos(π/8)=√(2+√2)/2

- trig -
**Vanessa**, Friday, July 1, 2011 at 5:12am
Okay, I understand how to get pi/8 but how do you figure pi/7 and how do you figure cos(10degrees) when you can use the sum and difference method of angles? Please help it is driving me crazy, and I have finals coming up. Need to get this down. Can I do the method about using pi/3 and pi/4 in the half angle formulas to find exact value of cos and sin of (pi/7)? I am so confused.

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