Question

How do I find the value of cos 11pi / 6?

Answer 1

Find `cos ((11pi)/6)`

Ans: `sqrt3/2`

Explanation:

Cal `cos ((11pi)/6) = cos t`

`cos 2t = cos ((22pi)/6) = cos ((-2pi)/6 + 12(2pi))` =
`= cos (-pi/3) = cos (pi/3) = 1/2`
Use trig identity: `cos 2t = 2cos^2 t - 1`

`2cos^2 t = 1 + 1/2 = 3/2`
`cos^2 t = 3/4`
`cos ((11pi)/6) = cos t = +- sqrt3/2`
Since the arc (11pi)/6 is located in Quadrant IV, only the positive answer is accepted.
`cos ((11pi)/6) = sqrt3/2`