The Inverse Trig Calculator is an online utility that computes the inverse values of trigonometric functions such as:
Inverse Sine (sin⁻¹ or arcsin)
Inverse Cosine (cos⁻¹ or arccos)
Inverse Tangent (tan⁻¹ or arctan)
Inverse Secant, Cosecant, and Cotangent
It tells you which angle produces a given trigonometric value, saving time and eliminating confusion around domains and ranges.
Inverse Trigonometric Functions
Inverse trigonometric functions reverse standard trigonometric operations.
Instead of:
angle → ratio
They calculate:
ratio → angle
Each inverse function has a restricted domain and range to ensure uniqueness.
Common inverse functions:
sin⁻¹(x) → arcsin(x)
cos⁻¹(x) → arccos(x)
tan⁻¹(x) → arctan(x)
These functions are widely used in equation solving, coordinate geometry, calculus, and real-world modeling.
Core Inverse Trigonometric Definitions (Highlighted):
sin⁻¹(x) = θ where sin(θ) = x
cos⁻¹(x) = θ where cos(θ) = x
tan⁻¹(x) = θ where tan(θ) = x
Domain Constraints:
−1 ≤ x ≤ 1 for sin⁻¹(x), cos⁻¹(x)
These constraints are automatically enforced by the calculator.Problem: Find sin⁻¹(0.5)
Step 1: Identify the inverse function
sin⁻¹(x)
Step 2: Check the domain
−1 ≤ 0.5 ≤ 1 (Valid)
Step 3: Determine the angle
sin(30°) = 0.5
Final Answer: sin⁻¹(0.5) = 30°