Trigonometric Ratios Calculator
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Trigonometric Ratios Calculator
Calculate Ratios
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Understanding Trigonometric Ratios
Trigonometry is a fundamental branch of mathematics that studies the relationships between the angles and sides of triangles. At its core are the trigonometric ratios, which are functions that relate an angle of a right-angled triangle to the ratio of the lengths of two of its sides.
The Six Trigonometric Ratios
For a right-angled triangle with an angle θ (theta), the primary trigonometric ratios are defined as follows:
Sine (sin θ): The ratio of the length of the side opposite the angle to the length of the hypotenuse (Opposite / Hypotenuse).Cosine (cos θ): The ratio of the length of the adjacent side to the angle to the length of the hypotenuse (Adjacent / Hypotenuse).Tangent (tan θ): The ratio of the length of the side opposite the angle to the length of the adjacent side (Opposite / Adjacent). This is also equal to sin θ / cos θ.
In addition to these primary ratios, there are three reciprocal ratios:
Cosecant (csc θ): The reciprocal of sine (1 / sin θ). It's Hypotenuse / Opposite.Secant (sec θ): The reciprocal of cosine (1 / cos θ). It's Hypotenuse / Adjacent.Cotangent (cot θ): The reciprocal of tangent (1 / tan θ). It's Adjacent / Opposite.
The Calculator's Functionality
This calculator takes an angle, which can be measured in either degrees or radians , and computes the values of these six trigonometric ratios. The mathematical functions used are built into most programming languages, but they typically expect angles in radians. Therefore, if you input an angle in degrees, the calculator first converts it to radians before applying the trigonometric functions.
Conversion Formula:
To convert degrees to radians: radians = degrees * (π / 180)
To convert radians to degrees: degrees = radians * (180 / π)
Why Use Trigonometric Ratios?
Trigonometric ratios are indispensable in many fields:
Navigation: Calculating distances and positions.Engineering: Designing structures, analyzing forces, and creating mechanical systems.Physics: Modeling wave phenomena (sound, light), analyzing projectile motion, and understanding oscillations.Astronomy: Measuring distances to celestial objects.Surveying: Determining land boundaries and elevations.Computer Graphics: Creating 2D and 3D animations and simulations.
Example Calculation:
Let's calculate the trigonometric ratios for an angle of 30 degrees :
First, convert 30 degrees to radians: 30 * (π / 180) = π / 6 radians.
sin(30°) = sin(π/6) ≈ 0.5 cos(30°) = cos(π/6) ≈ 0.866 tan(30°) = tan(π/6) ≈ 0.577 csc(30°) = 1 / sin(30°) ≈ 2.0 sec(30°) = 1 / cos(30°) ≈ 1.155 cot(30°) = 1 / tan(30°) ≈ 1.732
This calculator automates these computations, providing quick and accurate results.
function calculateTrigRatios() {
var angleInput = document.getElementById("angle");
var unitSelect = document.getElementById("unit");
var resultDiv = document.getElementById("result");
var angleValue = parseFloat(angleInput.value);
var unit = unitSelect.value;
resultDiv.classList.remove("visible"); // Hide previous results
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(angleValue)) {
resultDiv.innerHTML = "Please enter a valid number for the angle.";
resultDiv.classList.add("visible");
return;
}
var angleInRadians;
if (unit === "degrees") {
angleInRadians = angleValue * (Math.PI / 180);
} else {
angleInRadians = angleValue;
}
// Handle specific edge cases for division by zero
var sinValue = Math.sin(angleInRadians);
var cosValue = Math.cos(angleInRadians);
var tanValue = Math.tan(angleInRadians);
var cscValue = (sinValue === 0) ? "Undefined (division by zero)" : (1 / sinValue);
var secValue = (cosValue === 0) ? "Undefined (division by zero)" : (1 / cosValue);
var cotValue = (tanValue === 0) ? "Undefined (division by zero)" : (1 / tanValue);
// Round values for better readability
var sinRounded = typeof sinValue === 'number' ? sinValue.toFixed(6) : sinValue;
var cosRounded = typeof cosValue === 'number' ? cosValue.toFixed(6) : cosValue;
var tanRounded = typeof tanValue === 'number' ? tanValue.toFixed(6) : tanValue;
var cscRounded = typeof cscValue === 'number' ? cscValue.toFixed(6) : cscValue;
var secRounded = typeof secValue === 'number' ? secValue.toFixed(6) : secValue;
var cotRounded = typeof cotValue === 'number' ? cotValue.toFixed(6) : cotValue;
var resultHTML = "
Trigonometric Ratios: " +
"Sine (sin): " + sinRounded + "" +
"Cosine (cos): " + cosRounded + "" +
"Tangent (tan): " + tanRounded + "" +
"Cosecant (csc): " + cscRounded + "" +
"Secant (sec): " + secRounded + "" +
"Cotangent (cot): " + cotRounded + "";
resultDiv.innerHTML = resultHTML;
resultDiv.classList.add("visible");
}
function resetCalculator() {
document.getElementById("angle").value = "";
document.getElementById("unit").value = "degrees";
document.getElementById("result").innerHTML = "";
document.getElementById("result").classList.remove("visible");
}