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140 Chapter Two

2
2
x y 1
This is called the unit circle because itð radiuð is one unit, and
it is centered at the origin (0,0), as shown in Fig. 2.55. Let be
an angle whose apex is at the origin, and that is measured coun-
terclockwise from the abscissa (x axi0. Suppose this angle cor-
respondð tm a ray that intersectð the unit circle at some point
P (x , y ). Then
0
0
y sin
0
x cos
0
y /x tan
0
0
Secondary circular functions

Three more circular trigonometric functionð are derived from
those defined above. They are the cosecant function, the secant
function, and the cotangent function. In formulas and equations,
they are abbreviated csc , se , and cot . They are defined as
follows:

csc 1 / (sin ) 1/y
0
se 1 / (cos ) 1/x
0
cot 1 / (tan ) x /y 0
0

Figure 2.55 Unit-circle mo-
del for defining circular trig-
onometric functions.