SOLUTION: solve the following trigo equation. 2 cos(x)=-1 in the domain [0,2π]. i manage to do : cos(x)=-1/2 ref(x)=cos^-1 (1/2) =π/3 (

Algebra ->  Trigonometry-basics -> SOLUTION: solve the following trigo equation. 2 cos(x)=-1 in the domain [0,2π]. i manage to do : cos(x)=-1/2 ref(x)=cos^-1 (1/2) =π/3 (      Log On


   

Question 1078341: solve the following trigo equation. 2 cos(x)=-1 in the domain [0,2π].
i manage to do : cos(x)=-1/2
ref(x)=cos^-1 (1/2)
=π/3 (60degree)
but there are 2 answers please exlpain how do you get 2 answers from that π/3.
can you alo explain why we dont include the negative sign in the (1/2) to get the degree. the answers is 2π/3 and 4π/3 im sorry if my question is dump.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you mean dumb and not dump and no it is not.
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cos%28x%29=-1%2F2 means that it's in QII and QIII where the cosine is negative. So the reference angle is from 180 degrees(pi),
which is why you don't need to include the negative value but you have to remember to start from there and not from zero.
So 180%2B60=240 and 180-60=120.
Those are the equivalent degree values for the radian answers you provided.
Remember when you're on the unit circle, there will always be two answers for a sine or cosine value.