This document discusses key concepts in trigonometry including the unit circle, trigonometric functions, Taylor polynomials, quadrants, inverse functions, and the tangent function. It provides illustrations of the unit circle labeled with cosine and sine values, graphs of common trigonometric functions, a Taylor polynomial approximating sine, a sign chart for quadrants, and a graph of the tangent function showing its domain and periodic nature.

1. K.Anitha M.Sc.,Phil.,
A.Sujatha M.Sc.,Phil.,

2.  Unit Circles
 Trigonometric Functions
 Taylor’s Polynomial
 Quadrants
 Inverse function
 Tangent function

3. The unit circle, with some points labeled with their
cosine and sine (in this order), and the corresponding
angles in radians and degrees.

5. Trigonometric
functions: Sine, Cosine, Tangent, Cosecant
(dotted), Secant (dotted), Cotangent
(dotted)

7. The sine function (blue) is closely
approximated by its Taylor polynomial of
degree 7 (pink) for a full cycle centered on
the origin.

9. Signs of trigonometric functions in each
quadrant. The mnemonic
"all science teachers (are) crazy" lists the
functions which are positive from quadrants
I to IV.[5] This is a variation on the
mnemonic "All Students Take Calculus".

11.  Inverse Trigonometric Functions

13. Tangent Function: y=tan(x)
 One cycle occurs between -pi/2 and pi/2
 There are vertical asymptotes at each end of the
cycle. The asymptote that occurs at pi/2 repeats
every pi units.