Question #14b3d

1 Answer
Anjali G
Dec 22, 2016

#cot(2theta)+5costheta=2#

#cos(2theta)/sin(2theta)+5costheta=2#

#frac{cos^2theta-sin^2theta}{2sinthetacostheta}+5costheta=2#

#frac{cos^2theta-sin^2theta+(5costheta)*(2sinthetacostheta)}{2sinthetacostheta}=2#

#frac{cos^2theta-sin^2theta+10sinthetacos^2theta}{2sinthetacostheta}=2#

#frac{1-sin^2theta-sin^2theta+10sintheta(1-sin^2theta)}{2sinthetacostheta}=2#

#frac{1-2sin^2theta+10sintheta-10sin^3theta}{2sinthetacostheta}=2#

#-10sin^3theta-2sin^2theta+10sintheta+1=4sinthetacostheta#

Using a graphing calculator, I graphed each side of the equation to find the points of intersection.
#theta approx 1.036 +2pin#
#thetaapprox 1.74+2pin#
#thetaapprox 3.213+2pin#

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