Section 4.2 Trigonometric Functions: The Unit Circle
Jan 01, 2016
What you should learn:
• Identify a unit circle and describe its relationship to real numbers.
• Evaluate trigonometric functions using the unit circle.
• Use the domain and period to evaluate sine and cosine functions.
• Use a calculator to evaluate trigonometric functions.
Definitions of Trigonometric FunctionsLet t be a real number and let (x, y) be a point on the unit circle corresponding to t.
sin t = y
cos t = x
tan t = y/x, x ≠ o
cot t = x/y, y ≠ o
sec t = 1/x, x ≠ o
csc t = 1/y, y ≠ o
Domain and Period of Sine and Cosine
The domain of the sine and cosine functions is the set of real numbers. The range of the functions is from -1 to 1.
Definition of Periodic Function
A function f is periodic if there exists a positive real number c such that
f( t + c) = f(t)
for all t in the domain of f.
Odd Functions Even Functions
sin (-t) = -sin (t)
tan (-t) = -tan (t)
csc (-t) = -csc (t)
cot (-t) = -cot (t)
cos (-t) = cos (t)
sec (-t) = sec (t)