For the unit circle we have the situations pictured below; 90^circ and 180^circ are limits as the hypotenuse approaches the (positive) vertical axis and the (negative) horizontal axis respectively.
![enter image source here]()
By definition:
color(white)("XXX")sin=(color(green)("opposite"))/(color(red)("hypotenuse"))
color(white)("XXX")cos=(color(blue)("adjacent"))/(color(red)("hypotenuse"))
color(white)("XXX")tan=(color(green)("opposite"))/(color(blue)("adjacent"))
As limits we can see that
color(white)("XXX"){:
(sin(90^circ)=(color(green)1)/(color(red)1)=1,color(white)("xx"),sin(180^circ)=(color(green)0)/(color(red)(-1))=0),
(,,),
(cos(90^circ)=(color(blue)0)/(color(red)1)=0,,cos(180^circ)=(color(blue)(-1))/(color(red)1)=-1),
(,,),
(tan(90^circ)=(color(green)1)/(color(blue)0)" : undefined",,tan(180^circ)=(color(green)0)/(color(blue)(-1))=0)
:}
