How do you use the quadratic formula to solve #tan^2theta+3tantheta+1=0# for #0<=theta<360#?

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Answer 1 · 2016-11-22T19:17:42

#thetaapprox159.095#
#thetaapprox339.095#

#thetaapprox110.905#
#thetaapprox290.905#

Let #u=tantheta#
Rewrite the equation as:
#u^2+3u+1=0#

#u=frac{-(3)+-sqrt((3)^2-4(1)(1))}{2(1)}#
#u=frac{-3+-sqrt5}{2}#

Substitute u back in:
#tantheta=(-3+sqrt5)/2#
#theta=tan^-1((-3+sqrt5)/2)#

#thetaapprox159.095#
#thetaapprox339.095#

#tantheta=(-3-sqrt5)/2#
#theta=tan^-1((-3-sqrt5)/2)#

#thetaapprox110.905#
#thetaapprox290.905#