Question

How do you find the exact value of `cos [(-7pi)/6]`?

Answer 1

`cos((-7pi)/(6))=-(sqrt(3)/2)`

First step `cos(-7/6pi)=cos(7/6pi)` because cosine is an even function (for evry `x` `f(-x)=f(x)`)

Now you have to reduce `cos(7/6 pi)` to a value of a functon of an angle smaller than `pi/2` `rad`. To do this you use the formula
`cos(pi+x)= - cos(x)`. So you get `cos(7/6 pi)=-cos(pi/6)=-(sqrt(3))/2`