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Trigonometry 3a Inverse Trigonometric Ratios - arc-sin, arc-cos, arc-tan; Domains and Ranges, Principal Value Branches, Important Relations and Formulas

Trigonometry Tutorials: At a glance


    A Tutorial on Inverse Trigonometric Ratios

Target Audience: High School Students, College Freshmen and Sophomores, Class 11/12 Students in India preparing for ISC/CBSE and Entrance Examinations like the IIT-JEE, Anyone else who needs this Tutorial as a reference!

Inverse Trigonometric Ratios:

sin -1 X is an angle whose sine is X (and so on for the other ratios like cos-1, tan-1).The symbol sin-1a is often, written as "arc sin a"; similarly cos-1a is written" arc cos a," and so for the other inverse ratios. The value of an inverse trigonometric functions which lies in its principal value branch (range of principal inverse trigonometric functions) is called the principal value of that inverse trigonometric functions.

This Tutorial will introduce to you :

  • Domains and ranges (principal value branches) of inverse trigonometric functions.
  • Important formulas related to inverse trigonometric functions.
  • Graphs and plots of inverse trigonometric ratios.

In case you'd like to take a look at other Trigonometry tutorials : 

Trigonometry 1a ( Introduction to Trigonometry - Definitions, Formulas ) Introducing trigonometric ratios, plots of trigonometric functions, compound angle formulas. Domains and ranges of trigonometric functions, monotonicity of trigonometric functions quadrant wise. Formulas for double and triple angle ratios.

Trigonometry 1b ( Tutorial with solved problems based on Trigonometric ratios ) Problems based on the concepts introduced above.
Trigonometry 2a ( Basic concepts related to Heights and Distances ) Applying trigonometry to problems involving heights and distances. Angles of elevation and depression. Sine and Cosine rule, half angle formulas. Circumradius, inradius and escribed radius. Circumcentre, incentre, centroid and median of a triangle.

Trigonometry 2b ( Tutorial with solved problems related to Heights and Distances and other applications of Trigonometry ) - Problems based on the concepts introduced above.

Trigonometry 3a ( Introducing Inverse Trigonometric Ratios)
Inverse trigonometric ratios - their domains, ranges and plots. 

Trigonometry 3b ( Tutorial with solved problems related to inverse trigonometric ratios )- Problems related to inverse trigonometric ratios. 

Trigonometry 4 ( A tutorial on solving trigonometric equations )- Solving trigonometric equations. Methods and transformations frequently used in solving such equations.