Question #c2afe

2 Answers

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

Feb 14, 2018

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:

https://www.desmos.com/calculatorhttps://www.desmos.com/calculator

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.