SOLUTION: Find all solutions to the equation tan(t)=3/tan(t) in the interval 0≤t≤2π. First estimate the solutions from a graph, then find exact answers (given as fractions,

Algebra ->  Trigonometry-basics -> SOLUTION: Find all solutions to the equation tan(t)=3/tan(t) in the interval 0≤t≤2π. First estimate the solutions from a graph, then find exact answers (given as fractions,       Log On


   

Question 995822: Find all solutions to the equation tan(t)=3/tan(t) in the interval 0≤t≤2π. First estimate the solutions from a graph, then find exact answers (given as fractions, not decimals). Enter your answers as a comma separated list.
t=
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find all solutions to the equation tan(t)=3/tan(t) in the interval 0≤t≤2π. First estimate the solutions from a graph, then find exact answers (given as fractions, not decimals). Enter your answers as a comma separated list.
------
tan^2(t) = 3
---
tan(t) = sqrt(3)
---
t = arctan(sqrt(3)) = 30 degrees or t = 180+30 = 210 degrees
------------
Cheers,
Stan H.
-------------

Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find all solutions to the equation tan(t)=3/tan(t) in the interval 0≤t≤2π. First estimate the solutions from a graph, then find exact answers (given as fractions, not decimals). Enter your answers as a comma separated list.
--------------------------------------------------------------------

tan%5E2%28t%29 = 3.

tan(t) = +/- sqrt%283%29.

Solutions:

t = 60°  or  t = 240°       <<<--- for tan(t) = sqrt%283%29, and

t =  120°  or  t = 300°     <<<--- for tan(t) = -sqrt%283%29.