Why does sin(x) divided by sin(180-x) = 1

[Guest]

(working in degrees)

A bit confused why sin(x) / sin(180-x) = 1
e.g. sin(30)/sin(150) = 1
sin(40)/sin(140) = 1
sin(195)/sin(-15) = 1

What is the reason for this pattern? Thanks so much!

[romsek]

[tex]\sin(a-b) = \sin(a)\cos(b) - \cos(a)\sin(b)[/tex]

[tex]\sin(180^\circ-x) =\\
\sin(180^\circ)\cos(x) - \cos(180^\circ)\sin(x) = \\
0\cdot \cos(x) - (-1)\sin(x) = \\
\sin(x)\\~\\

\dfrac{\sin(x)}{\sin(180-x)} = \dfrac{\sin(x)}{\sin(x)} = 1[/tex]