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# cos (5pi/12) => exact value

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1. is there a way for me to work out cos (5pi/12) without using the cos-graph but only the "magic triangle" ?
thanks!
2. What in the world is the magic triangle?
3. Use the angles pi/4 and pi/6.
Not sure what a magic triangle is...you shouldn't need to resort to any magic to solve this one.
4. I meant the triangles where you can easily read the cos,sines of etc in surd form..
sorry, I dont quite understand your hint with the pi/4 pi/6 idea?
thanks again
5. Well, cos2A = 2cos²A - 1.

Let A = 5pi/12.

cos(5pi/6) = 2cos²(5pi/12) - 1.

Can you take it from here?

That's the triangle. Dunno if it's your magic one.
But you're looking to find the lengths cosAcosB and sinAsinB.

Well, fine. If you're going to do it the normal way, you might as well just say
5/12 = 1/4+1/6 and cos(A+B) = cosAcosB-sinAsinB.

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