Trigonometry Ratio Calculator

Trigonometry Ratio Calculator

Degrees Radians

Results:

Sine (sin):

Cosine (cos):

Tangent (tan):

Cosecant (csc):

Secant (sec):

Cotangent (cot):

function calculateTrigRatios() { var angleValue = parseFloat(document.getElementById("angleValue").value); var angleUnit = document.getElementById("angleUnit").value; if (isNaN(angleValue)) { document.getElementById("sinResult").innerText = "Please enter a valid number."; document.getElementById("cosResult").innerText = ""; document.getElementById("tanResult").innerText = ""; document.getElementById("cscResult").innerText = ""; document.getElementById("secResult").innerText = ""; document.getElementById("cotResult").innerText = ""; return; } var angleRad; if (angleUnit === "degrees") { angleRad = angleValue * Math.PI / 180; } else { // radians angleRad = angleValue; } var sinVal = Math.sin(angleRad); var cosVal = Math.cos(angleRad); var tanVal = Math.tan(angleRad); var epsilon = 1e-9; // For checking if a value is close to zero document.getElementById("sinResult").innerText = sinVal.toFixed(6); document.getElementById("cosResult").innerText = cosVal.toFixed(6); // Tangent (sin/cos) if (Math.abs(cosVal) < epsilon) { // tan is undefined when cos is 0 (e.g., 90, 270 degrees) document.getElementById("tanResult").innerText = "Undefined"; } else { document.getElementById("tanResult").innerText = tanVal.toFixed(6); } // Cosecant (1/sin) if (Math.abs(sinVal) < epsilon) { // csc is undefined when sin is 0 (e.g., 0, 180, 360 degrees) document.getElementById("cscResult").innerText = "Undefined"; } else { document.getElementById("cscResult").innerText = (1 / sinVal).toFixed(6); } // Secant (1/cos) if (Math.abs(cosVal) < epsilon) { // sec is undefined when cos is 0 document.getElementById("secResult").innerText = "Undefined"; } else { document.getElementById("secResult").innerText = (1 / cosVal).toFixed(6); } // Cotangent (cos/sin) if (Math.abs(sinVal) < epsilon) { // cot is undefined when sin is 0 document.getElementById("cotResult").innerText = "Undefined"; } else if (Math.abs(cosVal) < epsilon) { // cot is 0 when cos is 0 (and sin is not 0) document.getElementById("cotResult").innerText = (0).toFixed(6); // cot(90) = 0 } else { document.getElementById("cotResult").innerText = (1 / tanVal).toFixed(6); } } // Initial calculation on page load for default values document.addEventListener('DOMContentLoaded', function() { calculateTrigRatios(); });

Understanding Trigonometry Ratios

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. It is particularly focused on right-angled triangles, where the ratios of the sides are defined relative to the triangle's acute angles. These ratios are fundamental to many fields, including engineering, physics, architecture, and computer graphics.

The Six Trigonometric Ratios

For a right-angled triangle with an angle θ (theta):

  • Opposite Side: The side across from angle θ.
  • Adjacent Side: The side next to angle θ that is not the hypotenuse.
  • Hypotenuse: The longest side, opposite the right angle.

The six primary trigonometric ratios are:

1. Sine (sin θ)

The ratio of the length of the opposite side to the length of the hypotenuse.

sin(θ) = Opposite / Hypotenuse

2. Cosine (cos θ)

The ratio of the length of the adjacent side to the length of the hypotenuse.

cos(θ) = Adjacent / Hypotenuse

3. 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 = sin(θ) / cos(θ)

4. Cosecant (csc θ)

The reciprocal of the sine function. It is the ratio of the hypotenuse to the opposite side.

csc(θ) = 1 / sin(θ) = Hypotenuse / Opposite

5. Secant (sec θ)

The reciprocal of the cosine function. It is the ratio of the hypotenuse to the adjacent side.

sec(θ) = 1 / cos(θ) = Hypotenuse / Adjacent

6. Cotangent (cot θ)

The reciprocal of the tangent function. It is the ratio of the adjacent side to the opposite side, or cos(θ) / sin(θ).

cot(θ) = 1 / tan(θ) = Adjacent / Opposite = cos(θ) / sin(θ)

Degrees vs. Radians

Angles can be measured in two common units: degrees and 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 between them is: 180 degrees = π radians.

How to Use the Calculator

Simply enter the angle value you wish to analyze and select whether it's in degrees or radians. The calculator will instantly provide the values for all six trigonometric ratios, rounded to six decimal places. This tool is useful for students, engineers, and anyone needing quick trigonometric calculations.

Example Calculations:

Let's calculate the ratios for a 30-degree angle:

  • Input: Angle Value = 30, Angle Unit = Degrees
  • Sine (sin 30°): 0.500000
  • Cosine (cos 30°): 0.866025
  • Tangent (tan 30°): 0.577350
  • Cosecant (csc 30°): 2.000000
  • Secant (sec 30°): 1.154701
  • Cotangent (cot 30°): 1.732051

Now, consider an angle of π/2 radians (approximately 1.570796 radians or 90 degrees):

  • Input: Angle Value = 1.570796, Angle Unit = Radians
  • Sine (sin π/2): 1.000000
  • Cosine (cos π/2): 0.000000
  • Tangent (tan π/2): Undefined
  • Cosecant (csc π/2): 1.000000
  • Secant (sec π/2): Undefined
  • Cotangent (cot π/2): 0.000000

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