Question

Given that sin(0) = – 12/13, and 0 is in Quadrant III, what is sin(20)?

Answer 1

let use # to represent theta

Given that sin(#) = -12/13

# is in Quadrant III. we are to find sin(2#)

since sin(#) = opposite/hypotenus

Then, using pythagoras theorem

13^2 = 12^2 - x^2

169 = 144 - x^2

collecting like terms

x^2 = 169 - 144

x^2 = 25

x = 5

Therefore, cos(#) = -5/13

sin(2#) = 2sin#cos# (trigonometric rule)

sin(2#) = 2x - (12/13)x - (5/13)

= 120/169