 In this video, we provide the solution to question number eight for the practice exam number three for math 1060 We're asked to find all the solutions to the equation 2 cosine of 2 theta plus the square root of 3 Equals 0 and we want to do this in the interval Zero theta ranges from 0 to 360 degrees. So we're going to solve this in degrees here Let's first solve for the trigonometric function. We're going to subtract the square root of 3 from both sides So we get 2 cosine of 2 theta Equals negative root 3 we divide both sides by 2 we a cosine of 2 theta equals negative root 3 over 2 And so we want to think of when does cosine equal negative root 3 over 2 it is cosine of 2 theta so we might be thinking of using like a Double-angle identity of some kind that'll actually just make life more complicated for us Let's just think of it as we've changed the period So cosine is equal to negative negative in the second and third quadrant When is it equal to root 3 over 2 again in we're doing this in degrees? Well cosine will equal positive root 3 over 2 in the first quadrant that happens at a 30 degree angle So we're looking for those angles that reference 30 degrees in the second and third quadrant And so that's going to be a hundred and fifty degrees plus 360 k That's in the second quadrant because that's 180 minus 30 degrees then we have to do 180 plus 30 degrees Which is 210 plus 360 Right, but that's not equal to theta. That's equal to 2 theta So to solve for theta we have to divide this by 2 in which case 150 divided by 2 is 75 degrees then you get 180 k like so and then we have to also take 210 and Divide that by 2 as well 210 divided by 2 is going to give us a hundred and five And then we have to also add 180 to that as well Okay, so we definitely need to find an answer which includes 75 and 105 we see choice B has that notice that 255 That's 150 plus 180 Sorry, that's sorry. That's 75 plus 180 and then 285 is 105 plus 180 so the correct answer would then be choice B