Given that sin(b)=-2/3, and that b is in the third quadrant, what is the value of tan(2b)..?

1 Answer
Oct 4, 2017

Given sinb=-2/3," where "b in "III quadrant"

So cosb=-sqrt(1-sin^2b)=sqrt(1-4/9)=-sqrt5/3

Now tan(2b)=(sin2b)/(cos2b)

=(2sinbcosb)/(cos^2b-sin^2b)

=(2(-2/3)(-sqrt5/3))/(5/9-4/9)

=4sqrt5