How do you find the solution to 5sin^2theta+2sintheta=0 if 0<=theta<2pi?

1 Answer
Alan P.
Jan 9, 2017

theta in {0,2.730,3.146,5.872} (to 3 decimal places)

Explanation:

Given
color(white)("XXX")5sin^2(theta)+2sin(theta)=0

Factoring
color(white)("XXX")sin(theta) * (5sin(theta)+2)=0

rArr (for theta in (-pi/2,pi/2))
color(white)("XXX"){:(sin(theta)=0,color(white)("XX"),5sin(theta)+2=0), (rarr theta=0,,rarr sin(theta)=-2/5), (,,theta=-0.411516846 "( using calculator)") :}

Since sin(theta)=sin(theta+kpi), k in ZZ
for the specified domain, theta in [0,2pi)
color(white)("XXX"){: (theta= 0 or pi," or ",theta=pi-0.411516846 or 2pi-411516846), (,,theta=2.7300758075 or 5.8716684611) :}

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