How do you find the exact value of 2sin^2theta+3costheta-3=0 in the interval 0<=theta<360?

1 Answer
Nghi N
Dec 24, 2016

0, 60^@, 300^@, 360^@

Explanation:

Replace in the equation sin^2 t by (1 - cos^2 t) -->
2 - 2cos^2 t + 3cos t - 3 = 0
- 2cos^2 t + 3cos t - 1 = 0
Solve this quadratic equation for cos t.
Since a + b + c = 0, use shortcut. The 2 real roots are:
cos t = 1 and cos t = c/a = (-1)/(-2) = 1/2

Use trig table and unit circle -->
a. cos t = 1 --> arc t = 0 and t = 2pi
b. cos t = 1/2 --> arc t = +- pi/3
The co-terminal arc of (-pi/3) is (5pi)/3
Answers for (0, 2pi):
0, pi/3, (5pi)/3, 2pi, or
0, 60^@, 300^@, 360^@

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