Inverse Trig Calculator
Find the angle in degrees from a trigonometric ratio
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Bounded Oscillatory Function: Sine and cosine oscillate smoothly between -1 and +1 with period 360° (2π rad).
Variable Mechanics
Roles, constraints & impacts
Ratio Value
Input Angle / Ratio
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Bounded Oscillatory Function: Sine and cosine oscillate smoothly between -1 and +1 with period 360° (2π rad).
Common Mistakes & Traps
- Using Degree mode when Radians are expected (or vice versa).
- Tangent asymptotes at 90° and 270° (division by cos θ = 0 causes undefined infinity).
- Forgetting inverse trigonometric domain limits (e.g., arcsin input must be between -1 and 1).
Dimensional Analysis & Units
Ratio of side lengths → Dimensionless Scalar [-1, +1]
Real-World & Industry Application
Audio sound wave synthesis, AC alternating current electrical waveforms, robotic arm joint kinematics, and astronomical navigation.
Worked Example: Inverse Trig
Given:
- x = 0.5
- sin⁻¹(0.5) = 30°
- cos⁻¹(0.5) = 60°
- tan⁻¹(0.5) = 26.5651°
Answer: 30
Frequently Asked Questions
What is the Inverse Trig formula?
θ = sin⁻¹(x), cos⁻¹(x), tan⁻¹(x). Find the angle in degrees from a trigonometric ratio.
How do I calculate Inverse Trig?
Enter Ratio Value (x) into the calculator. It applies θ = sin⁻¹(x), cos⁻¹(x), tan⁻¹(x) and shows every step of the working.
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