How do you find the solution to 2sinthetacostheta+costheta=0 if 0<=theta<360?

1 Answer
Alan P.
Nov 21, 2016

theta in {90^@, 210^@,270^@, 330^@}

Explanation:

Factoring the left side of
color(white)("XXX")2sin(theta)cos(theta)+cos(theta)=0
gives
color(white)("XXX")color(red)(cos(theta)) * [color(blue)(2sin(theta)+1)] =0

Which implies (for theta in [0,360^@])
{: ("either",color(red)(cos(theta)=0),or,color(blue)(2sin(theta)+1=0)), (,rarr color(red)(theta=90^@ or 270^@),,rarr color(blue)(sin(theta)= -1/2)), (,,,rarr color(blue)(theta= 210^@ or 330^@)) :}

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