5.2 trigonometric functions: unit circle approach
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5.2Trigonometric 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)
(-1, 0)
(0, -1)
(1, 0)
y
x
(0, 1)
(-1, 0)
(0, -1)
(1, 0)
θ =ty
x
P = (a, b)
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 secant function is defined as
the tangent function is defined as If
If the cotangent function is defined as
(0, 1)
(-1, 0)
(0, -1)
(1, 0)
θ =t radiansy
x
P = (a, b)
If radians, the six trigonometric functions of the angle are defined as
y
x
r
a
b
Theorem
P=(a,b)
(5, 0)
Find the exact value of the remaining five trigonometric functions, given:
meaning
gives
P= (0,1)
x
y
θ
undefined
undefined
P= (1, 0)
P= (a, b)
x} r=1
undefined
undefined
a =1
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