Answer to Question #10219 in Calculus for m Khan

Question

Find all the solutions in the interval [0,2π) for the equation cos² x - 2cosx - 3 = 0
Show your Work.

Answer 1

Find all the solutions in the interval [0,2π) for the equation cos² x - 2cosx - 3 = 0.

cos² x - 2cosx - 3 = 0 ==>
(cos x + 1)(cos x - 3) = 0 ==>
cos x = -1& ==> x = π (= 180°);
cos x = 3 - impossible value.

The only value for x in the interval [0,2π) is π.