# If cos x=-1/3 and x is in (90,180), calculate sin x=?

Asked on by chezmena

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

cos x = -1/3

We kow that cosx= adjacent/ hypotenuse = -1/3

Then the oppsite = sqrt(3^2 - 1)= sqrt(8) = 2sqrt(2)

Then sinx = opposite/ hypotenuse = 2sqrt2/ 3

Since x is in the second quadrant, the  the sin is positive.

Then sinx = 2sqrt(2)/3

neela | High School Teacher | (Level 3) Valedictorian

Posted on

cosx =-1/3.

Therefore sine x =  +or - sqrt(1-cos^2x) = +or- sqrt(1-(-1/3)^2) = +or- sqrt(1-1/9) = +or- sqrt(8/9)

=+(2sqr2)/3,  as sine  is positive in (90 , 180)

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Because x is an angle located in the second quadrant, the value of the function sine is positive.

For finding the value of sine function, we'll use the fundamental formula of trigonometry:

(sin x)^2 + (cos x)^2 = 1

sin x = +sqrt[1-(cos x)^2]

sin x = +sqrt(1 - 1/9)

sin x = +sqrt(9-1)/9

sin x = +2sqrt2/3

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