Given that sin t= (-2/3) and that P(t) is a point in the 3rd quadrant, what is the cos of t?

1 Answer
Mar 9, 2018

Answer:

See explanation.

Explanation:

If we have #sin alpha# given, thento calculate #cos alpha# we use the identity:

#sin^2alpha+cos^2alpha=1#

If we substitute the given value we get:

#(-2/3)^2+cos^2alpha=1#

#4/9+cos^2alpha=1#

#cos^2alpha=1-4/9#

#cos^2alpha=5/9#

#cos alpha=-sqrt(5)/3 vv cos alpha=sqrt(5)/3#

The given equation has 2 solutions. To choose one we have to use the given information about the quadrant, in which the angle is located.

The angle is located in #Q3#. This means that its sine and cosine are both negative. Finally we can write the answer:

#cos alpha=-sqrt(5)/3#