If sin(θ) = − 5/6 with θ in Quadrant III, what is cos(θ)?

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1 Answer
Jan 28, 2018

cos(theta)=-sqrt(11)/6

Explanation:

sin(theta)=-5/6

We can build a right triangle in the unit circle,
with the hypotenuse 1 and a side sin(theta)=-5/6
(I recommend to make a sketch)

Then use Pythagoras (we deal with the sign afterwards)

cos(theta)=sqrt(1-(-5/6)^2)

=sqrt(36/36-25/36)

=sqrt(11/36)

=sqrt(11)/6

When we are in the third quadrant cos(theta)<0

Therefore

cos(theta)=-sqrt(11)/6