How do you find the solution to 3cos^2theta-4costheta+1=0 if 0<=theta<360?

1 Answer
Nghi N
Nov 29, 2016

0^@, 70^@53, 289^@47, 369^@

Explanation:

3cos^2 t - 4cos t + 1 = 0
Solve the quadratic equation for cos t.
We have: a = 3, b = -4, and c = 1.
Since a + b + c = 0, use shortcut. The 2 real roots are:
cos x = 1 and cos x = c/a = 1/3
a. cos x = 1 --> x = 0^@ or x = 360^@
b. cos x = 1/3 --> Calculator and unit circle give 2 solutions arcs:
x = 70^@53 and x = - 70^@53, or x = 289^@47 (co-terminal)

Answers for (0, 360):
0^@, 70^@53, 289^@47, 360^@

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