Trig Calculator Degrees

Trigonometric Calculator (Degrees)

Sine (sin) Cosine (cos) Tangent (tan) Cosecant (csc) Secant (sec) Cotangent (cot)

function calculateTrig() { var angleDegrees = parseFloat(document.getElementById('angleDegrees').value); var trigFunction = document.getElementById('trigFunction').value; var resultDiv = document.getElementById('trigResult'); var result; if (isNaN(angleDegrees)) { resultDiv.innerHTML = "Please enter a valid number for the angle."; return; } // Convert degrees to radians var angleRadians = angleDegrees * (Math.PI / 180); var epsilon = 1e-10; // Small value to check for near-zero denominators switch (trigFunction) { case 'sin': result = Math.sin(angleRadians); break; case 'cos': result = Math.cos(angleRadians); break; case 'tan': var cosVal = Math.cos(angleRadians); if (Math.abs(cosVal) < epsilon) { // Check if cosine is near zero (e.g., 90, 270 degrees) result = "Undefined (tan(" + angleDegrees + "°))"; } else { result = Math.tan(angleRadians); } break; case 'csc': var sinVal = Math.sin(angleRadians); if (Math.abs(sinVal) < epsilon) { // Check if sine is near zero (e.g., 0, 180, 360 degrees) result = "Undefined (csc(" + angleDegrees + "°))"; } else { result = 1 / sinVal; } break; case 'sec': var cosVal = Math.cos(angleRadians); if (Math.abs(cosVal) < epsilon) { // Check if cosine is near zero (e.g., 90, 270 degrees) result = "Undefined (sec(" + angleDegrees + "°))"; } else { result = 1 / cosVal; } break; case 'cot': var sinVal = Math.sin(angleRadians); var cosVal = Math.cos(angleRadians); if (Math.abs(sinVal) < epsilon) { // Check if sine is near zero (e.g., 0, 180, 360 degrees) result = "Undefined (cot(" + angleDegrees + "°))"; } else { result = cosVal / sinVal; // More robust than 1/tan(angleRadians) for edge cases } break; default: result = "Invalid function selected."; } if (typeof result === 'number') { resultDiv.innerHTML = "The " + trigFunction + " of " + angleDegrees + "° is: " + result.toFixed(8) + ""; } else { resultDiv.innerHTML = "Result: " + result + ""; } }

Understanding Trigonometric Functions in Degrees

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. It's fundamental in fields like engineering, physics, architecture, and even video game development. The most common trigonometric functions are sine, cosine, and tangent, along with their reciprocals: cosecant, secant, and cotangent.

What are Degrees?

Degrees are a unit of angular measurement, where a full circle is divided into 360 degrees. This system is widely used in everyday applications and geometry. While many scientific calculations use radians (where a full circle is 2π radians), degrees offer a more intuitive way to express angles for many practical purposes.

The Six Trigonometric Functions:

• Sine (sin): In a right-angled triangle, the sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.
• Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
• Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side (or sin/cos).
• Cosecant (csc): The reciprocal of sine (1/sin).
• Secant (sec): The reciprocal of cosine (1/cos).
• Cotangent (cot): The reciprocal of tangent (1/tan or cos/sin).

How to Use the Trigonometric Calculator

Our calculator simplifies the process of finding the value of these functions for any angle in degrees. Here's how to use it:

1. Enter the Angle: Input the angle you wish to calculate in the "Angle in Degrees" field. For example, you might enter 30, 90, or 180.
2. Select the Function: Choose the trigonometric function you want to apply from the "Select Function" dropdown menu (e.g., Sine, Cosine, Tangent).
3. Click Calculate: Press the "Calculate" button to see the result.

Examples of Calculations:

• Sine of 30 degrees: If you enter 30 and select 'Sine', the result will be 0.5.
• Cosine of 60 degrees: Entering 60 and selecting 'Cosine' will yield 0.5.
• Tangent of 45 degrees: Inputting 45 and choosing 'Tangent' will give you 1.0.
• Cosecant of 90 degrees: For 90 and 'Cosecant', the result is 1.0 (since sin(90) = 1).
• Tangent of 90 degrees: If you enter 90 and select 'Tangent', the calculator will correctly display "Undefined", as the tangent function is undefined at 90 degrees (and its odd multiples).

This calculator is a handy tool for students, educators, and professionals who need quick and accurate trigonometric values without manual calculation or conversion to radians.