Some Elementary Functions
Trigonometric Functions:

Unit Circle Definition of Trigonometric Functions: For any real number A, let P(A) be the point on the unit circle U. If the rectangular coordinates of P(A) are (x,y), then:


\cos{A}=x \ \ \ \ \ \ \sin{A}=y
 
if \ \ x \neq 0, \ \ \tan{A}={y \over x}={\sin{A} \over \cos{A}}
 
if \ \ y \neq 0,\ \ \cot{A}={x \over y}={\cos{A} \over \sin{A}}
 
if \ \ x \neq 0,\ \ \sec{A}={1 \over x}={1 \over \cos{A}}
 
if \ \ y \neq 0,\ \ \csc{A}={1 \over y}={1 \over \sin{A}}

 

Sine and cosine are defined for all real numbers. Ie; domain is   and Range is [-1,1]. See in the next Tclet, the graph of both sin(A) and cos(A) being graphed as you change A by dragging the red dot along the circumference..

The functions \tan{x} and \sec{x} are defined for all real x except when cos(x)=0. Ie; when x = {\pi \over 2} + n \pi (n is an integer).

From the graph bellow, see that Range(tan(x)) = and Range(sec(x)) =

 

 

 

tan(x) --

sec(x) --

The functions \cot{x} and \csc{x} are defined for all real x except when sin(x)=0. Ie; when x = {\pi \over 2} + n \pi (n is an integer).

In these cases, Range(cot(x)) = and Range(csc(x)) =

 

 

 

cot(x) --

csc(x) --

Trigonometric Identities:
Exercises:
 

 

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© 1998 Teresinha Kawasaki