How do you solve 2cos^2(t)+cos(t)=12cos2(t)+cos(t)=1?

1 Answer
Nghi N.
Jun 13, 2015

Solve; 2cos^2 t + cos t - 1 = 02cos2t+cost−1=0

Explanation:

Call cos x = p, and solve the quadratic equation:
y = v^2 + v - 1 = 0.y=v2+v−1=0.
Since a - b + c = 0, use shortcut: one real root is v = -1 and the other v = -c/a = 1/2.v=−ca=12.
Next solve the 2 basic equations: cos x = -1 and cos x = 1/2cosx=12
a. v = cos x = -1 -> x = pix=π
b. cos x = 1/2 -> x = +- pi/3 cosx=12→x=±π3

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
9572 views around the world
You can reuse this answer
Creative Commons License