Trigonometry question?

sin(pi + theta) = -0.345;

sin(2pi - theta) = -0.345;

sin(pi - theta) = 0.345.

theta acute angle  < 90 degrees -- 1st quadrant

pi + theta  -- 3rd quad  ...  sin is neg in quad 3

 sin(pi + theta) = -sin theta  =  -0.345

 2 pi - theta  is in quad 4

 again sin is neg

sin(2pi - theta) = -sin theta = -0.345

  pi - theta is in quad 2

 sin(pi - theta) = sin theta = +0.345

sin(θ) = 0.345

hint: sin(π) = sin(2π) = 0

think about a car on a circular track. It drives exactly π around the track to sin(π) = 0. then it goes a little farther π+θ. Now the car is below the equator.

sin (π+θ) = -0.345

the car drives all the way around to where it started then it backs up. again below the equator

sin(2π-θ) = -0.345

like the first. car drives half way, but this time it backs up. Above the equator.

sin(π - θ) = 0.345