Question

Question #c2afe

Answer 1

`cos ((-19pi)/6)` as `color(purple)(cos(-theta) = cos theta`

`=cos ((19pi)/6)`

`=cos (2pi + (5pi)/6)`

`=cos ((5pi)/6)` as `color(purple)(cos(2npi+theta)=costheta`

`=-sqrt3/2`

Answer 2

The result is `sqrt(3)/2`.

Explanation:

Since the cosine function has a period of `2pi` (which means it repeats itself every `2pi` units), we can add or subtract any multiples of `2pi` from the inside of the parentheses to make it easier to compute:

`color(white)=cos(-(19pi)/6)`

`=cos(-(19pi)/6+4pi)`

`=cos(-(19pi)/6+(24pi)/6)`

`=cos(-(19pi)/6+(24pi)/6)`

`=cos((5pi)/6)`

Here's that rotation on our unit circle:

We know that in this triangle with the `30^@` reference angle that the cosine ratio (adjacent over hypotenuse) is `(sqrt(3)/2)/1`, or just `sqrt(3)/2`.