Thread: Solving Quadratic Trigonometric Equations

How do you turn these equations: 2 sin x sec x - 2 sqrt(3) sin x = 0 and

(2 cos x + sqrt(3)) sin x = 0 into quadratic equation format?

Originally Posted by Devi09

How do you turn these equations: 2 sin x sec x - 2 sqrt(3) sin x = 0 and

(2 cos x + sqrt(3)) sin x = 0 into quadratic equation format?

Are you sure you want to put them into quadratic equation format? You can solve them by simply factoring.

You have a common factor of 2Sin(x) in the first equation:

2 Sin(x)(Sec(x) - sqrt(3))=0

Either Sin(x)=0
Or Sec(x)= Sqrt(3)

Etc... Can you clarify your question?

you have to solve each equation where 0 <= x <= 2pi. So the first one: sin x = 0 or sec = Sqrt(3). So find those in the unit circle and you got your answer?

as for the second one it's cos x = -Sqrt(3) / 2 or sin x = 0 and once again find those in the unit circle to get your answer I take it?

Originally Posted by Devi09

you have to solve each equation where 0 <= x <= 2pi. So the first one: sin x = 0 or sec = Sqrt(3). So find those in the unit circle and you got your answer?

as for the second one it's cos x = -Sqrt(3) / 2 or sin x = 0 and once again find those in the unit circle to get your answer I take it?

Yup.