Trigonometric Functions Calculator

Trigonometric Functions Calculator

function calculateTrigFunctions() { var angleValue = parseFloat(document.getElementById('angleValue').value); var angleUnit = document.getElementById('angleUnit').value; if (isNaN(angleValue)) { document.getElementById('sineResult').innerHTML = "Please enter a valid number for the angle."; document.getElementById('cosineResult').innerHTML = ""; document.getElementById('tangentResult').innerHTML = ""; return; } var angleInRadians; if (angleUnit === 'degrees') { angleInRadians = angleValue * (Math.PI / 180); } else { angleInRadians = angleValue; } var sine = Math.sin(angleInRadians); var cosine = Math.cos(angleInRadians); var tangent; // Handle tangent for angles where cosine is zero (e.g., 90, 270 degrees or pi/2, 3pi/2 radians) // Check if cosine is very close to zero to account for floating point inaccuracies if (Math.abs(cosine) < 1e-10) { // If cosine is effectively zero tangent = "Undefined"; } else { tangent = Math.tan(angleInRadians); } document.getElementById('sineResult').innerHTML = sine.toFixed(6); document.getElementById('cosineResult').innerHTML = cosine.toFixed(6); document.getElementById('tangentResult').innerHTML = (typeof tangent === 'number' ? tangent.toFixed(6) : tangent); }

Understanding 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 crucial in various fields, including geometry, physics, engineering, and computer graphics, for analyzing periodic phenomena and geometric relationships.

The Primary Functions: Sine, Cosine, and Tangent

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. It can also be expressed as tan(θ) = sin(θ) / cos(θ).
  tan(θ) = Opposite / Adjacent

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 commonly used in everyday geometry and navigation.
• Radians: A radian is 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 Trigonometric Functions Calculator simplifies finding the sine, cosine, and tangent of any given angle. Here's how to use it:

1. Enter Angle Value: Input the numerical value of the angle you wish to analyze into the "Angle Value" field.
2. Select Angle Unit: Choose whether your angle is in "Degrees" or "Radians" from the dropdown menu. This is crucial for accurate calculation.
3. Calculate: Click the "Calculate Functions" button.

The calculator will instantly display the sine, cosine, and tangent values for your specified angle. Note that for angles where the cosine is zero (e.g., 90° or 270°), the tangent will be "Undefined" as division by zero is not possible.

Examples:

• Example 1: Angle of 45 degrees
  • Input: Angle Value = 45, Angle Unit = Degrees
  • Output: Sine &approx; 0.707107, Cosine &approx; 0.707107, Tangent &approx; 1.000000
• Example 2: Angle of π/2 radians
  • Input: Angle Value = 1.570796 (approx. π/2), Angle Unit = Radians
  • Output: Sine &approx; 1.000000, Cosine &approx; 0.000000, Tangent = Undefined
• Example 3: Angle of 0 degrees
  • Input: Angle Value = 0, Angle Unit = Degrees
  • Output: Sine = 0.000000, Cosine = 1.000000, Tangent = 0.000000

This tool is perfect for students, engineers, and anyone needing quick and accurate trigonometric calculations.