6 Trigonometric Functions Calculator

6 Trigonometric Functions Calculator

Degrees Radians

Results

Sine (sin):
Cosine (cos):
Tangent (tan):
Cosecant (csc):
Secant (sec):
Cotangent (cot):
function calculateTrigFunctions() { var angleInput = document.getElementById("angleInput").value; var angleUnit = document.getElementById("angleUnit").value; var errorMessage = document.getElementById("errorMessage"); errorMessage.innerHTML = ""; // Clear previous errors if (isNaN(angleInput) || angleInput === "") { errorMessage.innerHTML = "Please enter a valid number for the angle."; document.getElementById("sineResult").innerHTML = ""; document.getElementById("cosineResult").innerHTML = ""; document.getElementById("tangentResult").innerHTML = ""; document.getElementById("cosecantResult").innerHTML = ""; document.getElementById("secantResult").innerHTML = ""; document.getElementById("cotangentResult").innerHTML = ""; return; } var angleValue = parseFloat(angleInput); var angleRad; if (angleUnit === "degrees") { angleRad = angleValue * (Math.PI / 180); } else { angleRad = angleValue; } var sinVal = Math.sin(angleRad); var cosVal = Math.cos(angleRad); var tanVal = Math.tan(angleRad); // Display results for primary functions document.getElementById("sineResult").innerHTML = sinVal.toFixed(6); document.getElementById("cosineResult").innerHTML = cosVal.toFixed(6); // Handle tangent edge cases (e.g., 90, 270 degrees) var tanResult; if (Math.abs(cosVal) < 1e-9) { // If cosine is very close to zero tanResult = "Undefined"; } else { tanResult = tanVal.toFixed(6); } document.getElementById("tangentResult").innerHTML = tanResult; // Calculate and display reciprocal functions var cscResult, secResult, cotResult; var epsilon = 1e-9; // Small value to check for "close to zero" // Cosecant (1/sin) if (Math.abs(sinVal) < epsilon) { cscResult = "Undefined"; } else { cscResult = (1 / sinVal).toFixed(6); } document.getElementById("cosecantResult").innerHTML = cscResult; // Secant (1/cos) if (Math.abs(cosVal) < epsilon) { secResult = "Undefined"; } else { secResult = (1 / cosVal).toFixed(6); } document.getElementById("secantResult").innerHTML = secResult; // Cotangent (1/tan or cos/sin) if (Math.abs(sinVal) < epsilon) { // If sine is very close to zero cotResult = "Undefined"; } else { cotResult = (cosVal / sinVal).toFixed(6); } document.getElementById("cotangentResult").innerHTML = cotResult; } // Calculate on load for default values document.addEventListener('DOMContentLoaded', function() { calculateTrigFunctions(); });

Understanding the 6 Trigonometric Functions

Trigonometric functions are fundamental mathematical functions that relate the angles of a right-angled triangle to the ratios of its side lengths. They are essential in various fields, including geometry, physics, engineering, and computer graphics. There are six primary trigonometric functions: sine, cosine, tangent, and their reciprocals: cosecant, secant, and cotangent.

The Primary Functions

Consider a right-angled triangle with an angle θ (theta). Let the side opposite to θ be 'opposite', the side adjacent to θ be 'adjacent', and the longest side be the 'hypotenuse'.

  • Sine (sin θ): The ratio of the length of the opposite side to the length of the hypotenuse.
    sin(θ) = Opposite / Hypotenuse
  • Cosine (cos θ): The ratio of the length of the adjacent side to the length of the hypotenuse.
    cos(θ) = Adjacent / Hypotenuse
  • Tangent (tan θ): The ratio of the length of the opposite side to the length of the adjacent side. It can also be expressed as sin(θ) / cos(θ).
    tan(θ) = Opposite / Adjacent

The Reciprocal Functions

These functions are the reciprocals of the primary trigonometric functions:

  • Cosecant (csc θ): The reciprocal of sine.
    csc(θ) = 1 / sin(θ) = Hypotenuse / Opposite
  • Secant (sec θ): The reciprocal of cosine.
    sec(θ) = 1 / cos(θ) = Hypotenuse / Adjacent
  • Cotangent (cot θ): The reciprocal of tangent.
    cot(θ) = 1 / tan(θ) = Adjacent / Opposite = cos(θ) / sin(θ)

Angle Units: Degrees vs. Radians

Angles can be measured in two common units:

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

Our calculator allows you to choose between these two units for your input angle.

How to Use the Calculator

  1. Enter Angle Value: Input the numerical value of your angle into the "Angle Value" field.
  2. Select Unit: Choose whether your angle is in "Degrees" or "Radians" from the dropdown menu.
  3. Calculate: Click the "Calculate Functions" button.
  4. View Results: The calculator will display the values for sine, cosine, tangent, cosecant, secant, and cotangent for your specified angle.

Examples

Let's look at some common angles:

  • Angle: 30 Degrees
    • sin(30°) = 0.5
    • cos(30°) &approx; 0.866025
    • tan(30°) &approx; 0.577350
    • csc(30°) = 2
    • sec(30°) &approx; 1.154701
    • cot(30°) &approx; 1.732051
  • Angle: π/2 Radians (90 Degrees)
    • sin(π/2) = 1
    • cos(π/2) = 0
    • tan(π/2) = Undefined (division by zero)
    • csc(π/2) = 1
    • sec(π/2) = Undefined (division by zero)
    • cot(π/2) = 0
  • Angle: 0 Radians (0 Degrees)
    • sin(0) = 0
    • cos(0) = 1
    • tan(0) = 0
    • csc(0) = Undefined (division by zero)
    • sec(0) = 1
    • cot(0) = Undefined (division by zero)

This calculator provides a quick and accurate way to find the values of these essential functions for any given angle, helping students, engineers, and mathematicians in their work.

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