Question 650299

Hi, 

I am just beginning Precalculus, and am confused about the process that involves solving for theta where there are actually two answers. I kind of understand the concept (the angle and its inverse, somehow) but do not know how to actually reach the two answers.

The problem I am looking at is cos (θ) = -√(3)/2

I have tried several methods that end in bizarre answers. Any help would be appreciated, thank you.

-Alex


cos (θ) = {{{- (sqrt(3))/2}}} ----- {{{cos^-1((- sqrt(3))/2)}}} = {{{-30^o}}}


As the angle is cos and < 0, {{{cos(- 30)}}} is in the 2nd quadrant, where its reference angle = {{{highlight_green(150^o)}}}, and in the 3rd quadrant where its reference angle = {{{highlight_green(210^o)}}}


OR


You could also look at the unit circle and see that:


{{{cos((- sqrt(3))/2)}}} = {{{150^o}}} and {{{210^o}}} in the 2nd and 3rd quadrants, respectively.


Send comments and “thank-yous” to “D” at MathMadEzy@aol.com