← CBSE Class 12
Inverse Trigonometric Functions
Chapter Overview
Inverse trigonometric functions sin^-1(x), cos^-1(x), tan^-1(x), etc. have restricted ranges to ensure single-valued outputs. The chapter covers principal value branches, properties including sin^-1(x) + cos^-1(x) = pi/2, and conversion between inverse functions.
Topics Covered
- Principal Values
- Domain and Range
- Properties of Inverse Trig
- Sum and Difference Formulas
- Conversion Between Functions
Key Formulas
sin^-1(x) + cos^-1(x) = pi/2
tan^-1(x) + tan^-1(y) = tan^-1((x+y)/(1-xy))
sin^-1(sin A) = A only when A in [-pi/2, pi/2]
Real-World Applications
Applications: Navigation, integration techniques, solving trigonometric equations in physics.
Study Tips
Tip: Memorize principal value ranges
Tip: Practice graph sketching
Tip: Learn conversion formulas