Question

How do you solve `2costheta+1<0`?

Answer 1

`((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)`