Question

Find the exact value
Find sin (2theta). Tan= 20/21. theta lies in quadrent 3

Answer 1

tan(theta) = oppo/adj = 2/3.
assume oppo = 2 and adj = 3. (you can assume them to be anything proportional to 2 and 3 respectively)
sin(theta) = oppo/hypo.
we know that oppo = 2.
by pythagoras theorem hypo = sqrt(oppo^2+adj^2)
therefore,hypo = sqrt(4+9) = 3.60555.
therefore sin(theta) = 2/3.60555 = 0.55.
but if theta is in third quadrant tan(theta) is positive while sin(theta) is negative.
therefore the answer is A) + or - 0.55.