Question

if sin theta = -12/13 and theta belongs to 4th quadrant find tan (2 theta)​

Answer 1

sin A = -12/13 = [p/h]

in fourth quadrant, p (ordinate) is -ve and b (abscissa) is +ve

b = √h^2 - p^2

b = √ 13^2 - (-12)^2

b = √169 - 144

b = √ 25

b = 5

tan A = [p/b] = -12/5

Tan 2A = 2 tan A / (1 - tan^2 A)

= 2*(-12/5) / (1 - (-12/5)^2

= -24/5 / (1 - 144/25)

= -24/5 / (25 - 144)/25

= -24/5 / -119/25

= 24*5/119

= 120/119