Cos Sin Tan Calculator

Trigonometric Function Calculator (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("sinResult").innerText = "Please enter a valid number."; document.getElementById("cosResult").innerText = "Please enter a valid number."; document.getElementById("tanResult").innerText = "Please enter a valid number."; return; } var angleInRadians; if (unitSelect === "degrees") { angleInRadians = angle * Math.PI / 180; } else { // radians angleInRadians = angle; } var sinValue = Math.sin(angleInRadians); var cosValue = Math.cos(angleInRadians); var tanValue; // Handle tangent for angles where cosine is zero (e.g., 90, 270 degrees) if (Math.abs(cosValue) < 1e-10) { // Check if cosine is very close to zero tanValue = "Undefined"; } else { tanValue = sinValue / cosValue; } document.getElementById("sinResult").innerText = sinValue.toFixed(6); document.getElementById("cosResult").innerText = cosValue.toFixed(6); if (tanValue === "Undefined") { document.getElementById("tanResult").innerText = tanValue; } else { document.getElementById("tanResult").innerText = tanValue.toFixed(6); } }

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 (sin), cosine (cos), and tangent (tan). These functions are crucial in various fields, including physics, engineering, architecture, and computer graphics.

What are Sine, Cosine, and Tangent?

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

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

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

Degrees vs. Radians

Angles can be measured in two primary units: degrees and radians.

• Degrees: A full circle is divided into 360 degrees. This is the most common unit for everyday use and geometry.
• Radians: A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. A full circle is 2π radians. Radians are often preferred in higher mathematics and physics because they simplify many formulas.

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

How to Use the 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" using 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. Note that for angles where the cosine is zero (e.g., 90° or 270°), the tangent will be "Undefined" because division by zero is not possible.

Examples

Let's look at some common angles:

• Angle: 0 Degrees
  • Sine (sin): 0.000000
  • Cosine (cos): 1.000000
  • Tangent (tan): 0.000000
• Angle: 30 Degrees
  • Sine (sin): 0.500000
  • Cosine (cos): 0.866025
  • Tangent (tan): 0.577350
• Angle: 45 Degrees
  • Sine (sin): 0.707107
  • Cosine (cos): 0.707107
  • Tangent (tan): 1.000000
• Angle: 90 Degrees
  • Sine (sin): 1.000000
  • Cosine (cos): 0.000000
  • Tangent (tan): Undefined
• Angle: π/2 Radians (equivalent to 90 degrees)
  • Sine (sin): 1.000000
  • Cosine (cos): 0.000000
  • Tangent (tan): Undefined

This calculator is a handy tool for students, educators, and professionals needing quick and accurate trigonometric function values.