Math + Fun !
Home  ::   About Us  ::   Tutor in Your Home  ::   Tutoring Center  ::   SUMMER CAMP  ::   Advertise With Us  ::   College Counseling  ::   Contact Us
Our online tests allow your kids to test their math skills. We make sure that your kids are having fun while studying by combining testing and practice sessions with cleverly designed math games.
Math is Fun
This site is an online mathematics and science school
where you can study without leaving your home (online education).
"Do not worry about your difficulties in mathematics, I assure you that mine are greater". Einstein, Albert (1879-1955)
Login  ::   Sign Up - FREE  ::   Refer a Friend
  School of Logical Thinking
  Tests Examples - Demo
  Elementary Mathematics
  High School Placement
  Placement College Test
  Flash Games
  ACT Assessment
  Test Description
  English Test
  Mathematics Test
  Reading Test
  Science Test
  Writing Test
  Early Mathematics
  Study Guide
Inverse trigonometric functions
The relation x = sin y permits to find both x by the given y , and also y by the given x ( at | x | ? 1 ). So, it is possible to consider not only a sine as a function of an angle, but an angle as a function of a sine. The last fact can be written as: y = arcsin x ( “arcsin” is read as “arcsine” ). For instance, instead of 1/2 = sin 30° it is possible to write: 30° = arcsin 1/2. At the second record form an angle is usually represented in a radian measure: / 6 = arcsin 1/2.

Definitions. arcsin x is an angle, a sine of which is equal to x. Analogously the functions arccos x, arctan x, arccot x, arcsec x, arccosec x are defined. These functions are inverse to the functions sin x, cos x, tan x, cot x, sec x, cosec x, therefore they are called inverse trigonometric functions. All inverse trigonometric functions are multiple-valued functions, that is to say for one value of argument an innumerable set of a function values is in accordance. So, for example, angles 30°, 150°, 390°, 510°, 750° have the same sine. A principal value of arcsin x is that its value, which is contained between – / 2 and + / 2 ( –90° and +90° ), including the bounds:
– / 2 ? arcsin x ? + / 2 .
A principal value of arccos x is that its value, which is contained between 0 and ( 0° and +180° ), including the bounds:
0 ? arccos x ? .
A principal value of arctan x is that its value, which is contained between – / 2 and + / 2 ( –90° and +90° ) without the bounds:
– / 2 < arctan x < + / 2 .
A principal value of arccot x is that its value, which is contained between 0 and ( 0° and +180° ) without the bounds:
0 < arccot x < .
If to sign any of values of inverse trigonometric functions as Arcsin x, Arccos x, Arctan x, Arccot x and to save the designations: arcsin x, arcos x, arctan x, arccot x for their principal values, then there are the following relations between them:
where k – any integer. At k = 0 we have principal values.

View My Stats
Math Plus Fun