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

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1 Answer
Jan 28, 2018

cos(θ)=116

Explanation:

sin(θ)=56

We can build a right triangle in the unit circle,
with the hypotenuse 1 and a side sin(θ)=56
(I recommend to make a sketch)

Then use Pythagoras (we deal with the sign afterwards)

cos(θ)=1(56)2

=36362536

=1136

=116

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

Therefore

cos(θ)=116