Question

Please, I need help. I don't understand how sin θ = sin (180 - θ). Can someone please explain it to me?

If sin(180 - theta) is an obtuse angle how can the angle be equal to sin(theta)?? I don't understand.

Answer 1

Draw any circle on coordinates system. Do your drawings accurately to understand forever.

Take one point of that circle. Connect it with the center and draw parallel lines with respect to x and y until ithey cross axes. Sin() is the value of y(from 0 to where your parallel line with respect to x-axis crossed y-axis). Now draw a 180-'theta' angle. If drawings are done accurately it will be clear for you why they are equal. So why that angles are equal then?

Well, if you add theta to your second angle you get 180 degrees, which is straight line, x axis indeed. That means you "lowered" 180 degrees with theta angle. As y "represents" value of sin and at both cases the 'height' of your triangles are at thesame height. Thus 'sins' of these 2 angles coincide.