How do you solve cosx=-1/sqrt2?

2 Answers
Dean R.
May 4, 2018

x = \pm 120^circ + 360^circ k

Explanation:

cos x = cos a has solutions x= \pm a + 360^circ k quad for integer k.

cos x = -1/sqrt{2} = cos( 120^circ)

x = \pm 120^circ + 360^circ k

Jim G.
May 4, 2018

"see explanation"

Explanation:

"since "cosx<0" then x is in second/third quadrants"

x=cos^-1(1/sqrt2)=pi/4larrcolor(red)"related acute angle"

rArrx=pi-pi/4=(3pi)/4larrcolor(red)"second quadrant"

"or "x=pi+pi/4=(5pi)/4larrcolor(red)"third quadrant"

"due to the periodicity of the cosine the solutions will"
"repeat every "2pi

color(blue)"solutions are"

x=(3pi)/4+2npito(n inZZ)

"or "x=(5pi)/4+2npito(n inZZ)

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