Inverse Sine (sin⁻¹) Calculator Online
Enter a value between -1 and 1 to calculate sin⁻¹ (arcsin). This tool provides instant results in both degrees and radians, with a step-by-step explanation.
sin⁻¹ Calculator
Output:
Step-by-step Explanation:
How the sin⁻¹ (Inverse Sine) Calculator Works
- The sin⁻¹ function, also called arcsin, is the inverse of the sine function. It takes a value (between -1 and 1) and returns the angle whose sine equals that value.
- Domain: [-1, 1]
- Range: [-π/2, π/2] (or -90° to 90°)
- Common use: Trigonometry, physics, engineering, and solving triangles.
Reference Table: Common sin⁻¹ Values
| Input (x) | sin⁻¹(x) in Degrees | sin⁻¹(x) in Radians |
|---|---|---|
| -1 | -90° | -π/2 (-1.5708) |
| -&sqrt;3/2 | -60° | -π/3 (-1.0472) |
| -&sqrt;2/2 | -45° | -π/4 (-0.7854) |
| -0.5 | -30° | -π/6 (-0.5236) |
| 0 | 0° | 0 |
| 0.5 | 30° | π/6 (0.5236) |
| &sqrt;2/2 | 45° | π/4 (0.7854) |
| &sqrt;3/2 | 60° | π/3 (1.0472) |
| 1 | 90° | π/2 (1.5708) |
sin⁻¹(x) Function Curve
A line graph showing the inverse sine function, where input values range from -1 to 1 (x-axis) and the angle output (y-axis) ranges from -90° to 90°.
User Guide: How to Use the sin⁻¹ Calculator
- Enter a number between -1 and 1.
- Click the "Calculate" button.
- See both numerical results and explanation steps.
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FAQs on sin⁻¹ Calculator
- Q1. What is sin⁻¹ on a calculator?
- A: Sin⁻¹ is the inverse sine (arcsin). It returns the angle whose sine equals the input.
- Q2. Can I input numbers greater than 1 or less than -1?
- A: No. The valid domain for arcsin is -1 ≤ x ≤ 1.
- Q3. Is the answer always in degrees?
- A: You can choose degrees or radians in the calculator.
- Q4. Where is sin⁻¹ used in real life?
- A: It’s used in navigation, engineering, signal processing, and solving right triangles.
- Q5. What’s the difference between sin and sin⁻¹?
- A: sin(θ): takes an angle and gives a ratio. sin⁻¹(x): takes a ratio and gives an angle.