SOLUTION: To the nearest degree, the values of x in the interval 0° &#8804; x < 360° that satisfy the equation 6 cos2 x – 7 cos x + 2 = 0 include all of the following except a.)48 b.)60

Algebra ->  Trigonometry-basics -> SOLUTION: To the nearest degree, the values of x in the interval 0° &#8804; x < 360° that satisfy the equation 6 cos2 x – 7 cos x + 2 = 0 include all of the following except a.)48 b.)60       Log On


   

Question 598873: To the nearest degree, the values of x in the interval 0° ≤ x < 360° that satisfy the equation 6 cos2 x – 7 cos x + 2 = 0 include all of the following except
a.)48
b.)60
c.)132
4.)312
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I vote for highlight%28132%5Eo%29 to be the choice that does not satisfy the equation.
I believe the equation was supposed to be
6%28cos%28x%29%29%5E2-7cos%28x%29%2B2=0
To solve it, I would make cos%28x%29=y and solve
6y%5E2-7y%2B2=0 whose solutions are both positive.
Factoring, I get
%283y-2%29%282y-1%29=0 with solutions y=2%2F3 and y=1%2F2
so I am looking for values of x (obviously in degrees) that will give me
cos%28x%29=1%2F2 and cos%28x%29=2%2F3
cos%2860%29=1%2F2 so 60%5Eo satisfies the equation.
312%5Eo=+362%5Eo-48%5Eo so cos%28312%5Eo%29=cos%28-48%5Eo%29=cos%2848%5Eo%29 so those two values must satisfy the equation if just one of the four choices does not.
I could verify to see if cos%2848%5Eo%29=2%2F3, but that would require a calculator.
Besides I know that cos%28312%5Eo%29=cos%28-48%5Eo%29=cos%2848%5Eo%29%3E0 while
cos%28132%5Eo%29=cos%28180%5Eo-48%5Eo%29=-cos%2848%5Eo%29%3C0