6 Trigonometric Functions Calculator
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6 Trigonometric Functions Calculator
Results
Sine (sin): N/A
Cosine (cos): N/A
Tangent (tan): N/A
Cotangent (cot): N/A
Secant (sec): N/A
Cosecant (csc): N/A
Understanding Trigonometric Functions
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The six fundamental trigonometric functions—sine, cosine, tangent, cotangent, secant, and cosecant—are essential tools in various fields, including physics, engineering, geometry, and calculus. They relate an angle of a right-angled triangle to the ratios of its side lengths.
The Six Trigonometric Functions Explained
Consider a right-angled triangle with an angle θ. The sides are:
- Opposite (O): The side opposite to the angle θ.
- Adjacent (A): The side adjacent to the angle θ (not the hypotenuse).
- Hypotenuse (H): The longest side, opposite the right angle.
The six trigonometric functions are defined as follows:
- Sine (sin θ): The ratio of the length of the opposite side to the length of the hypotenuse.
sin(θ) = O / H
- Cosine (cos θ): The ratio of the length of the adjacent side to the length of the hypotenuse.
cos(θ) = A / H
- Tangent (tan θ): The ratio of the length of the opposite side to the length of the adjacent side.
tan(θ) = O / A. It can also be expressed as tan(θ) = sin(θ) / cos(θ).
- Cotangent (cot θ): The reciprocal of the tangent function.
cot(θ) = A / O. It can also be expressed as cot(θ) = 1 / tan(θ) or cot(θ) = cos(θ) / sin(θ).
- Secant (sec θ): The reciprocal of the cosine function.
sec(θ) = H / A. It can also be expressed as sec(θ) = 1 / cos(θ).
- Cosecant (csc θ): The reciprocal of the sine function.
csc(θ) = H / O. It can also be expressed as csc(θ) = 1 / sin(θ).
Using the Calculator
This calculator allows you to input an angle and specify whether it is in degrees or radians. It then computes the values for all six trigonometric functions for that angle.
Use Cases
- Physics: Analyzing wave motion, projectile trajectories, and oscillations.
- Engineering: Designing structures, electrical circuits, and control systems.
- Navigation: Calculating distances and positions using angles.
- Geometry: Solving problems involving triangles and circles.
- Computer Graphics: Performing rotations and transformations in 2D and 3D space.
Example Calculation
Let's calculate the trigonometric functions for an angle of 45 degrees:
- Sine (sin 45°): Approximately 0.7071
- Cosine (cos 45°): Approximately 0.7071
- Tangent (tan 45°): Approximately 1.0
- Cotangent (cot 45°): Approximately 1.0
- Secant (sec 45°): Approximately 1.4142
- Cosecant (csc 45°): Approximately 1.4142
If the angle was specified in radians, for example, π/4 radians (which is equivalent to 45 degrees), the results would be identical.
function calculateTrigFunctions() {
var angleValueInput = document.getElementById("angleValue");
var angleUnitSelect = document.getElementById("angleUnit");
var angleValue = parseFloat(angleValueInput.value);
var angleUnit = angleUnitSelect.value;
var sinResultSpan = document.querySelector("#sineResult span");
var cosResultSpan = document.querySelector("#cosineResult span");
var tanResultSpan = document.querySelector("#tangentResult span");
var cotResultSpan = document.querySelector("#cotangentResult span");
var secResultSpan = document.querySelector("#secantResult span");
var cscResultSpan = document.querySelector("#cosecantResult span");
// Clear previous results
sinResultSpan.textContent = "N/A";
cosResultSpan.textContent = "N/A";
tanResultSpan.textContent = "N/A";
cotResultSpan.textContent = "N/A";
secResultSpan.textContent = "N/A";
cscResultSpan.textContent = "N/A";
// Input validation
if (isNaN(angleValue)) {
alert("Please enter a valid number for the angle value.");
return;
}
var angleInRadians;
if (angleUnit === "degrees") {
angleInRadians = angleValue * (Math.PI / 180);
} else { // radians
angleInRadians = angleValue;
}
// Calculate trigonometric functions
var sinValue = Math.sin(angleInRadians);
var cosValue = Math.cos(angleInRadians);
// Handle potential division by zero for tan, cot, sec, csc
var tanValue = (cosValue === 0) ? "Undefined" : (sinValue / cosValue);
var cotValue = (sinValue === 0) ? "Undefined" : (cosValue / sinValue);
var secValue = (cosValue === 0) ? "Undefined" : (1 / cosValue);
var cscValue = (sinValue === 0) ? "Undefined" : (1 / sinValue);
// Set results, formatting to a reasonable number of decimal places
sinResultSpan.textContent = typeof sinValue === 'number' ? sinValue.toFixed(6) : sinValue;
cosResultSpan.textContent = typeof cosValue === 'number' ? cosValue.toFixed(6) : cosValue;
tanResultSpan.textContent = typeof tanValue === 'number' ? tanValue.toFixed(6) : tanValue;
cotResultSpan.textContent = typeof cotValue === 'number' ? cotValue.toFixed(6) : cotValue;
secResultSpan.textContent = typeof secValue === 'number' ? secValue.toFixed(6) : secValue;
cscResultSpan.textContent = typeof cscValue === 'number' ? cscValue.toFixed(6) : cscValue;
}