Question

evaluate sin [arctan(-4/9)] I know the answer i just dont know how to do it. Please help

Answer 1

So lets try letting u=arctan(-4/9)
Then tan(u)=-4/9
so build this triangle in the right quadrant then find the hyp.
then find sin(u)

Answer 2

how do i choose whether it is in the 2nd or 4th quadrant

Answer 3

we know u is between -pi/2 and pi/2
so I will tell you the correct quadrant
the correct quadrant is the fourth since those angle values will be between -pi/2 and 0 (which is a subset of between -pi/2 and pi/2) and definitely because your tan value is negative

Answer 4

we choose 4th
because it is between -pi/2 and pi/2 and tan is negative

Answer 5

where is -pi/2 on the unit circle?

Answer 6

-pi/2<=arctan<=pi/2