How do you solve 2cosx-sqrt3=0?

1 Answer
MathFact-orials.blogspot.com
Nov 18, 2016

pi/6+-n2pi, (5pi)/6+-n2pi

Explanation:

We have:

2cosx-sqrt3=0

We can simplify it this way:

2cosx=sqrt3

cosx=sqrt3/2

x=pi/6=30^o

Ok, so we have our reference angle. Now let's apply it to a coordinate system.

Cosine is positive in Q1 and in Q4.

In Q1, we have the angle already as pi/6. Since there is no constraint on the solution, the general solution is pi/6+-n2pi, where n is a natural number

In Q4, the angle is 2pi-pi/6=(5pi)/6 and again we need to show the general solution of (5pi)/6+-n2pi with n again being a natural number.

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