Question

Find the following in exact form??

cos `pi/3`

sin `(7pi)/6`

Answer 1

`cos(pi/3)=1/2`

`sin((7pi)/6) = -1/2`

Explanation:

The angles in the first quadrant usually lead to known values - you may have some table for these values.

Anyway, we have

`cos(pi/3)=1/2`

For the other quadrants, we usually find a relation with angles belonging to the first. For example, `(7pi)/6` is a bit more than `pi`: you may write it as

`(7pi)/6 = \frac{(6+1)pi}{6} = pi + \frac{pi}{6}`

Using the identity

`sin(pi+alpha) = -sin(alpha)`

we have

`sin(pi + \frac{pi}{6}) = -sin(pi/6)`

Again, `pi/6` belongs to the first quadrant, and thus is a known value: `-sin(pi/6) = -1/2`