How do you solve 2costheta+1<0?

1 Answer
Nghi N
Jul 23, 2017

((2pi)/3, (4pi)/3)

Explanation:

2cos t + 1 < 0 --> cos t < - 1/2
First, solve: 2cos t + 1 = 0
cost = - 1/2.
Trig table gives t = +- (2pi)/3, or
t = (2pi)/3 and t = (4pi)/3 (co-terminal to -(2pi)/3)
Now, solve the trig inequality by the unit circle.
cos t < - 1/2 when the arc t varies between (2pi)/3 and (4pi)/3.
(2pi)/3 < t < (4pi)/3
Answer by interval: ((2pi)/3, (4pi)/3)

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