How do you find the exact value of $2cosx+1=0$ in the interval $0<=x<360$ ?

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How do you find the exact value of $2cosx+1=0$ in the interval $0<=x<360$ ?

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Answer 1 · 2017-07-21T09:41:01

$x=120^@" or "x=240^@$

Explanation:

$"isolate " cosx^@$

$"subtract 1 from both sides"$

$rArr2cosx^@=-1$

$"divide both sides by 2"$

$rArrcosx^@=-1/2$

$rArrx=cos^-1(1/2)=60^@larrcolor(red)" related acute angle"$

$"since "cosx^@<0" then x in second / third quadrant"$

$rArrx=(180-60)=120^@larrcolor(red)" in second quadrant"$

$rArrx=(180+60)=240^@larrcolor(red)" in third quadrant"$

$rArrx=120^@" or " x=240^@to0<= x< 360$

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How do you find the exact value of $2cosx+1=0$ in the interval $0<=x<360$ ?

1 Answer

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How do you find the exact value of $2cosx+1=0$ in the interval $0<=x<360$ ?