sin(arctan(-4/3)

Question

okay so i made arctan(-4/3) = x
so im solving for sin(x)
and x= arctan(-4/3)
so then tanx = -4/3

and now im stuck i don't know what to do after that

Answer 1

Draw the right triangle (3,4,5)
3^2+4^2 = 9+16 = 25 = 5^2
angle A = atan(4/3)
sin A = 4/5
now look for quadrant
tan = -4/3 in quadrant 2 and in quadrant 4
in quadrant 2 sin A = 4/5
in quadrant 4 sin A = -4/5

Answer 2

just draw the triangle
tan = y/x
sin = y/h

h = 5 (3-4-5 triangle!)

principal value of arctan(-4/3) is in QIV.

sin = -4/5