SOLUTION: Solve the equation for the solution in the interval [0. 2pi) {{{tan^3 (x) = 3 tan (x)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation for the solution in the interval [0. 2pi) {{{tan^3 (x) = 3 tan (x)}}}       Log On


   

Question 678908: Solve the equation for the solution in the interval [0. 2pi)
tan%5E3+%28x%29+=+3+tan+%28x%29
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
tan%5E3+%28x%29+=+3+tan+%28x%29
tan%5E3+%28x%29+-+3+tan+%28x%29+=+0
tan%28x%29%28tan%5E2+%28x%29+-+3%29+=+0
tan%28x%29+=+0 or tan%5E2+%28x%29+-+3+=+0
tan%28x%29+=+0 or tan%5E2+%28x%29+=+3
tan%28x%29+=+0 or tan%28x%29+=+sqrt%283%29 or tan%28x%29+=+-sqrt%283%29

From tan%28x%29+=+0 we get:
x+=+0+%2B+2pi%2An
x+=+pi+%2B+2pi%2An
From tan%28x%29+=+sqrt%283%29 we get:
x+=+pi%2F3+%2B+2pi%2An
x+=+4pi%2F3+%2B+2pi%2An
From tan%28x%29+=+-sqrt%283%29 we get:
x+=+-pi%2F3+%2B+2pi%2An
x+=+2pi%2F3+%2B+2pi%2An

These six equations represent the general solution. (IOW all the possible solutions to your equation.) The n's in these equations integers. Replacing the n's with various integers will give you various x's that are solutions to your equation. I'll leave it up to you to try different n's to find the x's that are in the interval [0, 2pi) (Hint: Each equation will provide only one x value that is in the interval.)