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

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

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Answer 1 · 2017-07-23T00:52:14

#((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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How do you solve #2costheta+1<0#?

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