Sine Cosine Tangent Calculator

Sine, Cosine, Tangent Calculator

Degrees Radians

Results:

Sine:

Cosine:

Tangent:

function calculateTrigFunctions() { var angleInput = document.getElementById("angleInput").value; var unitSelect = document.getElementById("unitSelect").value; var angle = parseFloat(angleInput); if (isNaN(angle)) { document.getElementById("sineResult").innerHTML = "Please enter a valid number."; document.getElementById("cosineResult").innerHTML = ""; document.getElementById("tangentResult").innerHTML = ""; return; } var angleInRadians; if (unitSelect === "degrees") { angleInRadians = angle * Math.PI / 180; } else { // radians angleInRadians = angle; } var sineValue = Math.sin(angleInRadians); var cosineValue = Math.cos(angleInRadians); var tangentValue = Math.tan(angleInRadians); document.getElementById("sineResult").innerHTML = sineValue.toFixed(6); document.getElementById("cosineResult").innerHTML = cosineValue.toFixed(6); // Handle tangent for angles where it's undefined (e.g., 90, 270 degrees, pi/2, 3pi/2 radians) // Check if cosine is very close to zero to avoid floating point issues if (Math.abs(cosineValue) < 1e-9) { document.getElementById("tangentResult").innerHTML = "Undefined"; } else { document.getElementById("tangentResult").innerHTML = tangentValue.toFixed(6); } } // Run calculation on page load with default values window.onload = calculateTrigFunctions;

Understanding Sine, Cosine, and Tangent

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The three fundamental trigonometric functions are Sine, Cosine, and Tangent. These functions are crucial in various fields, including physics, engineering, navigation, and computer graphics.

The Basics: Right-Angled Triangles

In a right-angled triangle, these functions relate the angles to the ratios of its sides:

  • Hypotenuse: The longest side, opposite the right angle.
  • Opposite: The side directly across from the angle you are considering.
  • Adjacent: The side next to the angle you are considering (not the hypotenuse).

A common mnemonic to remember these ratios is SOH CAH TOA:

  • SOH: Sine = Opposite / Hypotenuse
  • CAH: Cosine = Adjacent / Hypotenuse
  • TOA: Tangent = Opposite / Adjacent

Beyond Right Triangles: The Unit Circle

While initially defined for right triangles, sine, cosine, and tangent can be extended to any angle using the unit circle. The unit circle is a circle with a radius of 1 centered at the origin (0,0) of a coordinate plane. For any point (x, y) on the unit circle corresponding to an angle θ (measured counter-clockwise from the positive x-axis):

  • Sine (sin θ) is the y-coordinate of the point.
  • Cosine (cos θ) is the x-coordinate of the point.
  • Tangent (tan θ) is the ratio y/x (or sin θ / cos θ).

This extension allows us to calculate trigonometric values for angles greater than 90 degrees or even negative angles.

Degrees vs. Radians

Angles can be measured in two primary units:

  • Degrees: A full circle is 360 degrees. This is commonly used in geometry and everyday applications.
  • Radians: A full circle is 2π radians. Radians are often preferred in higher mathematics, physics, and engineering because they simplify many formulas and calculations, especially those involving calculus.

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

How to Use This Calculator

Our Sine, Cosine, Tangent Calculator makes it easy to find the trigonometric values for any given angle:

  1. Enter Angle Value: Input the numerical value of your angle into the "Angle Value" field.
  2. Select Angle Unit: Choose whether your angle is in "Degrees" or "Radians" from the dropdown menu.
  3. Click Calculate: Press the "Calculate" button.

The calculator will instantly display the Sine, Cosine, and Tangent values for your specified angle, rounded to six decimal places.

Examples

Let's look at some common angles:

  • Angle: 45 Degrees (or π/4 Radians)
    • Sine (45°) ≈ 0.707107
    • Cosine (45°) ≈ 0.707107
    • Tangent (45°) = 1.000000
  • Angle: 30 Degrees (or π/6 Radians)
    • Sine (30°) = 0.500000
    • Cosine (30°) ≈ 0.866025
    • Tangent (30°) ≈ 0.577350
  • Angle: 90 Degrees (or π/2 Radians)
    • Sine (90°) = 1.000000
    • Cosine (90°) ≈ 0.000000
    • Tangent (90°) = Undefined (as cos(90°) is 0, and division by zero is undefined)

Use this calculator to quickly find these values for any angle you need!

Leave a Reply

Your email address will not be published. Required fields are marked *