Use a compound angle formula to determine the exact value of cos ( 11π/12 )?

Question

can you please show me how to do this

Answer 1

Zhan,

I agree with Douglas.

cos(11pi/12)=cos (8pi/12+3pi/12)=cos(8pi/12)*cos3pi/12)-sin(8pi/12)*sin(3pi/12)

cos(11pi/12)=(-1/2)*.707-(3^(1/2)/2)*.707

.707=2^(1/2)/2

Answer 2

Think about what you know. There are only a few angles of which we know the exact values of cosine. These are the angles on the unit circle:

0,pi/6,pi/4,pi/3,pi/2,2pi/3,3pi/4,5pi/6,pi.

These are all the exact angles up to pi.

Now, you need to figure out how to write 11pi/12 in terms of the above angles (as a sum).

Once you do this, you can use an angle-sum identity to determine cos(11pi/12).