SOLUTION: I am stuck on this problem where I need to solve for X. (tan^-1) 2x= -pi/6 If anyone could help it would be much appreciated!

Algebra ->  Trigonometry-basics -> SOLUTION: I am stuck on this problem where I need to solve for X. (tan^-1) 2x= -pi/6 If anyone could help it would be much appreciated!      Log On


   

Question 293273: I am stuck on this problem where I need to solve for X.
(tan^-1) 2x= -pi/6
If anyone could help it would be much appreciated!
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I am stuck on this problem where I need to solve for X.
(tan^-1) 2x= -pi/6
----
That equation says "the angle whose tangent is 2x is -pi/6"
Find the tangent of both sides to get:
2x = tan(-pi/6)
2x = -1/sqrt(3)
---
x = -1/(2sqrt(3)
======================
Cheers,
Stan H.
=======================

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... Start with the given equation.


... Take the tangent of both sides to eliminate the inverse tangent.


... Break up the tangent into sine over cosine


... Evaluate the sine of -pi%2F6 to get -1%2F2


... Evaluate the cosine of -pi%2F6 to get sqrt%283%29%2F2


... Multiply the first fraction by the reciprocal of the second fraction.


... Multiply and simplify


... Rationalize the denominator of the fraction on the right side.


... Divide both sides by 2.


So the solution is x=-sqrt%283%29%2F6


Edit: Take note that -sqrt%283%29%2F6=-1%2F%282%2Asqrt%283%29%29 (just do a bit of algebraic manipulation)