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DEFINITIONS OF THE TRIGONOMETRIC
FUNCTIONS IN TERMS OF A CIRCLE
FROM THE CIRCLE, CENTRED AT THE ORIGIN, WITH
RADIUS r , WE HAVE, FOR ANY POINT ( x , y ) ON THE
CIRCLE, THE FOLLOWING:
x2 + y2 = r 2 .
THE DEFINITIONS OF THE TRIGONOMETRIC
FUNCTIONS IN TERMS OF THIS CIRCLE ARE AS
FOLLOWS:
CONSIDER THE ANGLE θ , MEASURED IN RADIANS, AS
SHOWN:
THEN sinθ =
y
x
, cosθ = ,
r
r
y
x
, if x ≠ 0 , cot θ = , if y ≠ 0 ,
x
y
r
r
secθ = , if x ≠ 0 AND cscθ = , if y ≠ 0 .
x
y
tanθ =
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