SOLUTION: How do I find the cos(5pi/12)?! The question says "Use the sum or difference formula to determine the value of the trigonometric function" Thank you!

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Question 863135: How do I find the cos(5pi/12)?! The question says "Use the sum or difference formula to determine the value of the trigonometric function"
Thank you!
Found 2 solutions by Alan3354, lwsshak3:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
5pi/12 = 3pi/12 + 2pi/12 = pi/4 + pi/6
That's how you do it.

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
How do I find the cos(5pi/12)?! The question says "Use the sum or difference formula to determine the value of the trigonometric function"
***
cos(5π/12)=cos(2π/12+3π/12)=cos(π/6+π/4)
Identity: cos(x+y)=cosxcosy-sinxsiny)
cosx=cos(π/6)=√3/2
cosy=cos(π/4)=√2/2
sinx=sin(π/6)=1/2
siny=sin(π/4)=√2/2
cos(x+y)=√3/2*√2/2-1/2*√2/2=√6/4-√2/4=(√6-√2)/4
...
calculator check:
cos(5π/12)≈0.2588�
exact value=(√6-√2)/4≈0.2588�