Can anyone help me with a trig math problem??

Question

If sin (@ ) = -0.3678, explain how to get the value of @ in radians in the third quadrant.

- I was doing sin^(-1) = -.3678, but Im not sure if thats how u find it for the third quad. Any help would be great, thanks!!!

Answer 1

Yes, take the arcsin. But try this: take the arcsin of POSITIVE .3678, then do pi + (that answer). That value lies in the third quadrant, and is the value @ you seek.

Steve

Answer 2

Given:
sin (@ ) = -0.3678
sin(π - @) = -sin (@ ) = 0.3678
π - @ = arcsin(0.3678)
@ = π - arcsin(0.3678)
@ = π - 0.376642 ≈ π - 3π/8
@ = 2.76495 rad ≈ 5π/8 = 158.42°