6 Trig Functions Calculator

6 Trigonometric Functions Calculator

Results:

Sine (sin):
Cosine (cos):
Tangent (tan):
Cosecant (csc):
Secant (sec):
Cotangent (cot):
function calculateTrigFunctions() { var angleValue = parseFloat(document.getElementById('angleValue').value); var unitDegrees = document.getElementById('angleUnitDegrees').checked; var angleRad; // Clear previous results document.getElementById('resultSin').textContent = "; document.getElementById('resultCos').textContent = "; document.getElementById('resultTan').textContent = "; document.getElementById('resultCsc').textContent = "; document.getElementById('resultSec').textContent = "; document.getElementById('resultCot').textContent = "; if (isNaN(angleValue)) { alert('Please enter a valid number for the angle.'); return; } if (unitDegrees) { angleRad = angleValue * (Math.PI / 180); } else { angleRad = angleValue; } var sinVal = Math.sin(angleRad); var cosVal = Math.cos(angleRad); // Use a small epsilon for floating point comparisons to avoid issues near zero var epsilon = 1e-9; document.getElementById('resultSin').textContent = sinVal.toFixed(8); document.getElementById('resultCos').textContent = cosVal.toFixed(8); // Tangent if (Math.abs(cosVal) < epsilon) { // cos(x) is zero, tan is undefined document.getElementById('resultTan').textContent = 'Undefined'; } else { document.getElementById('resultTan').textContent = (sinVal / cosVal).toFixed(8); } // Cosecant if (Math.abs(sinVal) < epsilon) { // sin(x) is zero, csc is undefined document.getElementById('resultCsc').textContent = 'Undefined'; } else { document.getElementById('resultCsc').textContent = (1 / sinVal).toFixed(8); } // Secant if (Math.abs(cosVal) < epsilon) { // cos(x) is zero, sec is undefined document.getElementById('resultSec').textContent = 'Undefined'; } else { document.getElementById('resultSec').textContent = (1 / cosVal).toFixed(8); } // Cotangent if (Math.abs(sinVal) < epsilon) { // sin(x) is zero, cot is undefined document.getElementById('resultCot').textContent = 'Undefined'; } else { document.getElementById('resultCot').textContent = (cosVal / sinVal).toFixed(8); } }

Understanding the 6 Trigonometric Functions

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. It's fundamental in fields like physics, engineering, navigation, and computer graphics. The six basic trigonometric functions are sine, cosine, tangent, cosecant, secant, and cotangent.

The Six Functions Explained

For a right-angled triangle with an angle θ:

  • Sine (sin θ): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
    sin(θ) = Opposite / Hypotenuse
  • Cosine (cos θ): The ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
    cos(θ) = Adjacent / Hypotenuse
  • Tangent (tan θ): The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
    tan(θ) = Opposite / Adjacent = sin(θ) / cos(θ)

The other three functions are the reciprocals of sine, cosine, and tangent, respectively:

  • 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)

Degrees vs. Radians

Angles can be measured in two primary units: degrees or radians. It's crucial to know which unit you're working with, as the numerical value of the angle will differ, and trigonometric functions in most programming languages (like JavaScript's Math.sin()) expect radians.

  • Degrees: A full circle is 360 degrees.
  • Radians: A full circle is 2π radians. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.

The conversion factor is: 180 degrees = π radians.

How to Use the Calculator

  1. Enter Angle Value: Input the numerical value of the angle you want to analyze.
  2. Select Unit: Choose whether your angle is in "Degrees" or "Radians" using the radio buttons.
  3. Calculate: Click the "Calculate Functions" button.

The calculator will then display the values for sine, cosine, tangent, cosecant, secant, and cotangent for the given angle. If a function is undefined for a particular angle (e.g., tangent of 90 degrees), it will indicate "Undefined".

Examples

Let's look at some common angles:

  • Angle: 30 degrees
    • sin(30°) = 0.5
    • cos(30°) &approx; 0.8660254
    • tan(30°) &approx; 0.5773503
    • csc(30°) = 2
    • sec(30°) &approx; 1.1547005
    • cot(30°) &approx; 1.7320508
  • Angle: π/2 radians (90 degrees)
    • sin(π/2) = 1
    • cos(π/2) = 0
    • tan(π/2) = Undefined
    • csc(π/2) = 1
    • sec(π/2) = Undefined
    • cot(π/2) = 0
  • Angle: 0 radians (0 degrees)
    • sin(0) = 0
    • cos(0) = 1
    • tan(0) = 0
    • csc(0) = Undefined
    • sec(0) = 1
    • cot(0) = Undefined

This calculator provides a quick and easy way to determine the values of these essential trigonometric functions for any given angle.

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