Cos(-11/12) use the sum or difference formula to find the exact number
To find the exact value of cos(-11/12) using the sum or difference formula, we'll first need to know the cosines of two angles that we can combine to get -11/12.
The sum formula for cosine states that cos(A + B) = cos(A)cos(B) - sin(A)sin(B).
Now, let's find two angles whose cosine values we know. It will be helpful to remember that the cosine function is an even function, meaning that cos(-x) = cos(x). So, if we can find an angle A such that cos(A) = cos(11/12), we can use the sum formula to find the exact value we're looking for.
To find A, we can use the fact that if the cosine of an angle is x, then the cosine of the angle's supplementary angle (180 degrees - the angle) is also x.
So, let's find an angle that has a cosine of 11/12: A = cos^(-1)(11/12) (using the inverse cosine function).
Using a calculator, we find that A ≈ 0.421.
Now, we can use the sum formula: cos(-11/12) = cos(A - 180) = cos(A)cos(180) - sin(A)sin(180) = cos(A)(-1) - sin(A)(0) = -cos(A).
Substituting the known value of A, we find cos(-11/12) = -cos(0.421) ≈ -0.911.
Therefore, the exact value of cos(-11/12) using the sum or difference formula is approximately -0.911.