Question #74a3a

1 Answer
Nghi N
Apr 5, 2017

pi/2; (7pi)/6; (11pi/6)

Explanation:

2sin t - 1 = 1/(sin t)
sin^2 t - sin t - 1 = 0.
Solve this quadratic equation for sin t.
Because a + b + c = 0, use shortcut. The 2 real roots are:
sin t = 1 and sin t = c/a = - 1/2
Use trig table and unit circle:
a. sin t = 1 --> t = pi/2
b. sin t = - 1/2 --> 2 solutions -->
t = - pi/6, or t = (11pi)/6 (co-terminal), and
t = pi - (-pi/6) = pi + pi/6 = (7pi)/6
Answers for (0, 2pi):
pi/2; (7pi)/6; (11pi)/6

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