Sine Inverse Calculator
Calculate Sine Inverse (arcsin)
Results
Radians: 0.52
Input Sine Value: 0.50
What is Sine Inverse?
The sine inverse function, also known as arcsin, is the inverse operation of the sine function. It answers the question: “What angle has a sine equal to a given value?”. For example, the sine of 30° is 0.5. Therefore, the sine inverse of 0.5 is 30°. The notation for sine inverse is sin⁻¹(x) or arcsin(x). This calculator helps you find the sine inverse in both degrees and radians.
Sine Inverse Formula and Mathematical Explanation
The sine inverse is defined as: If sin(θ) = x, then θ = sin⁻¹(x). The domain of the sine inverse function is [-1, 1], and its range is [-90°, 90°] or [-π/2, π/2] in radians.
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| x | The value of the sine | Dimensionless | -1 to 1 |
| θ | The angle | Degrees or Radians | -90° to 90° or -π/2 to π/2 |
Practical Examples
Example 1: You’re using your phone’s calculator and need to find the angle whose sine is 0.866. You would enter 0.866 and use the sin⁻¹ function. The result would be approximately 60°.
Example 2: In a physics problem, you might need to find the angle of a ramp, and you know the ratio of the opposite side to the hypotenuse is 0.707. Using the sine inverse function, you would find the angle is 45°.
How to Use This Sine Inverse Calculator
- Enter the sine value in the input field. This value must be between -1 and 1.
- The calculator will automatically display the sine inverse in degrees and radians.
- The chart will also update to show the relationship between the sine value and the angle.
Key Factors That Affect Sine Inverse Results
- Input Value: The primary factor is the input sine value. The closer the value is to 1 or -1, the closer the angle will be to 90° or -90°.
- Unit of Measurement: The result can be expressed in degrees or radians. This calculator provides both.
Frequently Asked Questions (FAQ)
- How do I find the sine inverse on my phone’s calculator?
- Most phone calculators have a scientific mode. You may need to rotate your phone to landscape to access it. Look for a “2nd” or “inv” button, which will change the “sin” button to “sin⁻¹”.
- What is the difference between sine and sine inverse?
- Sine takes an angle and gives you a ratio, while sine inverse takes a ratio and gives you an angle.
- What is arcsin?
- Arcsin is another name for the sine inverse function.
- Why is the input for sine inverse limited to -1 to 1?
- The sine of any angle can only be between -1 and 1, so the input for its inverse function is limited to this range.
Related Tools and Internal Resources
- Cosine Calculator – Find the cosine of an angle.
- Tangent Calculator – Find the tangent of an angle.
- Radians to Degrees Converter – Convert angles from radians to degrees.