5.2
Trigonometric Functions:
Unit Circle Approach
The unit circle is a circle whose radius is
1 and whose center is at the origin.
Since r = 1:
becomes
(0, 1)
y
(-1, 0)
(1, 0)
(0, -1)
x
(0, 1)
y
 t
P = (a, b)
(-1, 0)
(1, 0)
(0, -1)
x
Let t be a real number and let P = (a, b)
be the point on the unit circle that
corresponds to t.
The sine function associates with t the
y-coordinate of P and is denoted by
The cosine function associates with t the
x-coordinate of P and is denoted by
If
the tangent function is defined as
If
the tangent function is defined as
If
the secant function is defined as
If
the cotangent function is defined as
(0, 1)
y
  t radians
P = (a, b)
(-1, 0)
(1, 0)
(0, -1)
x
If
radians, the six trigonometric
functions of the angle are defined as
y
a
b
r
x
Theorem
Find the exact value of the remaining five
trigonometric functions, given:
P=(a,b)
(5, 0)
meaning
gives
y
undefined
P= (0,1)

x
undefined
r 1

x
P= (1, 0)
P= (a, b)
undefined
undefined
a =1