Inverse Trigonometric Functions Calculator
Calculate all inverse trigonometric functions: arcsin, arccos, arctan, arccot, arcsec, arccsc
Calculate Inverse Trigonometric Functions
Returns the angle whose sine is the given value
Domain: -1 ≤ x ≤ 1
Results
Function Information
Example: Finding an Angle in a Right Triangle
Problem
In a right triangle, the opposite side is 2 cm and the hypotenuse is 4 cm. Find the angle θ.
Solution
We know that sin(θ) = opposite/hypotenuse = 2/4 = 0.5
To find θ, we use the inverse sine function:
θ = arcsin(0.5)
θ = 0.5236 radians = 30°
Therefore, the angle is 30°
Inverse Trigonometric Functions
Common Values
Quick Tips
Check domain restrictions before calculating
Results are always within the principal range
Use inverse functions to find angles from ratios
arctan and arccot accept all real numbers
Understanding Inverse Trigonometric Functions
What are Inverse Trigonometric Functions?
Inverse trigonometric functions are the inverse operations of trigonometric functions. While trigonometric functions take an angle and return a ratio, inverse trigonometric functions take a ratio and return an angle.
Applications
- •Engineering: Calculate angles in structures and mechanisms
- •Physics: Determine angles in wave and motion problems
- •Navigation: Calculate bearings and directions
- •Computer graphics: Rotation and transformation calculations
Domain and Range
Each inverse trigonometric function has specific domain and range restrictions to ensure they are well-defined functions (one-to-one mapping).
Key Points:
- • Domain restrictions prevent undefined values
- • Range values are principal values
- • Results are unique within the specified range
- • Always verify input is within valid domain
Important: Inverse trigonometric functions return angles in their principal ranges. For other angle solutions, add appropriate multiples of the period.