How do you solve #Sin 2 theta + cos theta = 0#?

1 Answer
Alan P.
Jun 18, 2016

Assuming an interval of #[0,2pi]#
#theta in {pi/2,(3pi)/2,(7pi)/6,(11pi)/6}#

Explanation:

Using the double angle formula:
#color(white)("XXX")sin(2theta)=2sin(theta)cos(theta)#

#sin(2theta)+cos(theta)=0#

#rArr 2sin(theta)cos(theta)+cos(theta)=0#

#rArr(cos(theta))*(2sin(theta)+1)=0#

#rArr# (within the interval #theta in [0,2pi]#)
#color(white)("XXX"){: (cos(theta)=0,color(white)("XXX")"or"color(white)("XXX"),2sin(theta)+1=0), (rarrcolor(white)("X")theta=pi/2" or " (3pi)/2,,rarrcolor(white)("X")sin(theta)=-1/2), (,,rarrcolor(white)("X")theta=(7pi)/6" or "(11pi)/6) :}#

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