How do you find all solutions in the interval [0,2pi) of the equation (cosx)^2 - 2.6 cosx - 0.87 =0?

1 Answer
Nghi N.
Mar 17, 2016

107^@46 and 152^@54

Explanation:

Solve the quadratic equation for cos x, using the improved quadratic formula.
D = d^2 = b^2 - 4ac = 6.76 + 3.48 = 10.24 --> d = +- 3.20
cos x = -b/(2a) +- d/(2a) = 1.3 +- 1.6
cos x = 2.9 (rejected as > 1)
cos x = - 0.3 --> x = +- 107^@46.
Answer for (0, 2pi):

107^@46 and (360 - 107.46) = 252^@54 (co-terminal)

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
2429 views around the world
You can reuse this answer
Creative Commons License