| The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages. |
|
Home  Trigonometric Functions Inverse Trigonometric Functions Theorem 3: |
|
 Search the VIAS Library | Index
|
  |
Theorem 3:
THEOREM 3 (i) (ii) (iii) From part (i), arcsin x and -arccos x must differ only by a constant. We already knew this from Example 5, arcsin x = -arccos x + π/2. Before now we were not able to find the area of the regions under the curves
It is a remarkable and quite unexpected fact that these areas are given by inverse trigonometric functions.
|
|
| Home Trigonometric Functions Inverse Trigonometric Functions Theorem 3: |
|
= arcsin x + C = -arccos x + C. (Provided that |x| < 1).
= arctan x + C = -arccot x + C.
= arcsecx + C = -arccsc x + C. (Provided that |x| > 1).
,
, 
Last Update: 2006-11-05