# `3tan^2 (x) + 4tan(x) - 4 = 0` Use the Quadratic Formula to solve the equation in the interval `0,2pi)`. Then use a graphing utility to approximate the angle `x`.

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Expert Answers

gsarora17 | Certified Educator

`3tan^2(x)+4tan(x)-4=0`

using quadratic formula,

`tan(x)=(-4+-sqrt(4^2-4*3*(-4)))/(2*3)`

`tan(x)=(-4+-sqrt(16+48))/6`

`tan(x)=(-4+-8)/6=-2 , 2/3`

solutions for tan(x)=-2 for the range `0<=x<=2pi` are

`x=pi-arctan(2) , 2pi-arctan(2)`

solutions for tan(x)=2/3 for the range `0<=x<=2pi` are,

`x=pi+arctan(2/3) , arctan(2/3)`

See the attached graph

x `~~` 0.6 , 2 , 3.7 , 5.2