Expert: Paul Klarreich - 2/10/2009

Question
Use factoring, the quadratic formula, or identities to solve the equation. Find all solutions in the interval [0, 2π) and list them in increasing order.

5cos^2x + 17cosx = 12

(2 possible answers)
x=
x=




When I factored these out I got 3/5 and 4. However, neither work.. please help! thanks.

Answer
Questioner:   brooke
Category:  Calculus
Private:  No
 
Subject:  question.
Question:  Use factoring, the quadratic formula, or identities to solve the equation. Find all solutions in the interval [0, 2π) and list them in increasing order.

5cos^2x + 17cosx = 12

(2 possible answers)
x=
x=




When I factored these out I got 3/5 and 4. However, neither work.. please help! thanks.
............................
No, you got 3/5 and  -4. (not 4)
Which means you got cos x = 3/5 and  cos x = -4.

Now you will need your calculator to find arccos(3/5).
I assume you know enough not to ask the calculator to find arccos(-4).