Inverse Trig on Calculator

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Inverse Trigonometric Function Calculator

Arcsine (asin) Arccosine (acos) Arctangent (atan)
For Arcsine/Arccosine, value must be between -1 and 1.
Degrees Radians
function calculateInverseTrig() { var trigFunction = document.getElementById("trigFunction").value; var ratioValueInput = document.getElementById("ratioValue").value; var outputUnit = document.getElementById("outputUnit").value; var resultDiv = document.getElementById("inverseTrigResult"); var ratioValue = parseFloat(ratioValueInput); if (isNaN(ratioValue)) { resultDiv.innerHTML = "Please enter a valid number for the Ratio Value."; return; } var angle; var unitText = ""; switch (trigFunction) { case "asin": if (ratioValue 1) { resultDiv.innerHTML = "Error: Arcsine input must be between -1 and 1."; return; } angle = Math.asin(ratioValue); break; case "acos": if (ratioValue 1) { resultDiv.innerHTML = "Error: Arccosine input must be between -1 and 1."; return; } angle = Math.acos(ratioValue); break; case "atan": angle = Math.atan(ratioValue); break; default: resultDiv.innerHTML = "An unexpected error occurred. Please select a function."; return; } if (outputUnit === "degrees") { angle = angle * (180 / Math.PI); unitText = " degrees"; } else { unitText = " radians"; } resultDiv.innerHTML = "The angle is: " + angle.toFixed(4) + unitText + ""; }

Understanding Inverse Trigonometric Functions

Inverse trigonometric functions, often called arc functions, are essential tools in mathematics, physics, and engineering. While standard trigonometric functions (sine, cosine, tangent) take an angle and return a ratio, inverse trigonometric functions do the opposite: they take a ratio and return the corresponding angle.

What are Arcsine, Arccosine, and Arctangent?

  • Arcsine (asin or sin⁻¹): If sin(θ) = x, then arcsin(x) = θ. It tells you the angle whose sine is x. The input 'x' (ratio value) must be between -1 and 1, and the output angle is typically in the range of -π/2 to π/2 radians (-90° to 90°).
  • Arccosine (acos or cos⁻¹): If cos(θ) = x, then arccos(x) = θ. It tells you the angle whose cosine is x. The input 'x' (ratio value) must also be between -1 and 1, and the output angle is typically in the range of 0 to π radians (0° to 180°).
  • Arctangent (atan or tan⁻¹): If tan(θ) = x, then arctan(x) = θ. It tells you the angle whose tangent is x. Unlike arcsine and arccosine, the input 'x' (ratio value) can be any real number, and the output angle is typically in the range of -π/2 to π/2 radians (-90° to 90°).

Degrees vs. Radians

Angles can be measured in two primary units: degrees and radians. Our calculator allows you to choose your preferred output unit:

  • Degrees: A full circle is 360 degrees. This unit is commonly used in everyday applications and geometry.
  • Radians: A full circle is 2π radians. Radians are the standard unit for angles in advanced mathematics, calculus, and many scientific fields because they simplify many formulas.

The conversion between them is straightforward: 180 degrees = π radians.

How to Use the Inverse Trigonometric Function Calculator

  1. Select Function: Choose whether you want to calculate Arcsine, Arccosine, or Arctangent from the dropdown menu.
  2. Enter Ratio Value: Input the numerical ratio for which you want to find the angle. Remember the domain restrictions for Arcsine and Arccosine (values between -1 and 1).
  3. Select Output Unit: Choose whether you want the result in Degrees or Radians.
  4. Click "Calculate Angle": The calculator will instantly display the corresponding angle.

Examples:

  • Finding an angle with Arcsine: If you know the sine of an angle is 0.5, select "Arcsine", enter "0.5" as the Ratio Value, and choose "Degrees". The calculator will show 30 degrees. If you choose "Radians", it will show approximately 0.5236 radians (which is π/6).
  • Finding an angle with Arccosine: If the cosine of an angle is 0.7071 (approximately 1/√2), select "Arccosine", enter "0.7071", and choose "Degrees". The result will be approximately 45 degrees.
  • Finding an angle with Arctangent: If the tangent of an angle is 1, select "Arctangent", enter "1", and choose "Degrees". The result will be 45 degrees.

This calculator simplifies the process of finding angles from trigonometric ratios, making it a valuable tool for students, engineers, and anyone working with trigonometry.

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