Trigonometric Calculator
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f8f9fa;
color: #333;
line-height: 1.6;
margin: 0;
padding: 20px;
}
.loan-calc-container {
max-width: 800px;
margin: 30px auto;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
border: 1px solid #e0e0e0;
}
h1, h2 {
color: #004a99;
text-align: center;
margin-bottom: 25px;
}
.input-group {
margin-bottom: 20px;
padding: 15px;
border: 1px solid #dee2e6;
border-radius: 5px;
background-color: #fdfdfd;
display: flex;
flex-wrap: wrap;
align-items: center;
gap: 15px;
}
.input-group label {
font-weight: bold;
color: #004a99;
flex-basis: 150px; /* Fixed width for labels */
text-align: right;
margin-right: 10px;
}
.input-group input[type="number"],
.input-group select {
flex-grow: 1;
padding: 10px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 1rem;
min-width: 150px; /* Ensure inputs have a minimum width */
}
.btn-calculate {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #28a745;
color: white;
border: none;
border-radius: 5px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
.btn-calculate:hover {
background-color: #218838;
}
#result {
margin-top: 30px;
padding: 20px;
background-color: #e9ecef;
border: 1px solid #ccc;
border-radius: 5px;
text-align: center;
}
#result h3 {
margin-top: 0;
color: #004a99;
}
#result-value {
font-size: 2.5rem;
font-weight: bold;
color: #28a745;
display: block; /* Make it a block for better spacing */
margin-top: 10px;
}
.explanation {
margin-top: 40px;
border-top: 1px solid #e0e0e0;
padding-top: 30px;
}
.explanation h2 {
text-align: left;
margin-bottom: 20px;
}
.explanation p, .explanation ul, .explanation li {
margin-bottom: 15px;
color: #555;
}
.explanation code {
background-color: #e9ecef;
padding: 3px 6px;
border-radius: 3px;
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
}
@media (max-width: 768px) {
.input-group {
flex-direction: column;
align-items: stretch;
}
.input-group label {
text-align: left;
margin-bottom: 5px;
flex-basis: auto;
}
.input-group input[type="number"],
.input-group select {
width: 100%;
}
.loan-calc-container {
padding: 20px;
}
}
Trigonometric Calculator
Result:
—
Understanding Trigonometric Calculations
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. In particular, it's concerned with trigonometric functions, which describe these relationships. The most fundamental trigonometric functions are sine (sin), cosine (cos), and tangent (tan), defined for a right-angled triangle relative to one of its acute angles.
The Six Trigonometric Functions:
- Sine (sin): The ratio of the length of the side opposite the angle to the length of the hypotenuse.
- Cosine (cos): The ratio of the length of the adjacent side to the angle to the length of the hypotenuse.
- Tangent (tan): The ratio of the length of the side opposite the angle to the length of the adjacent side. It can also be expressed as
sin(angle) / cos(angle).
- Cosecant (csc): The reciprocal of sine.
csc(angle) = 1 / sin(angle).
- Secant (sec): The reciprocal of cosine.
sec(angle) = 1 / cos(angle).
- Cotangent (cot): The reciprocal of tangent.
cot(angle) = 1 / tan(angle) or cos(angle) / sin(angle).
Units of Measurement:
Angles in trigonometry can be measured in two primary units:
- Degrees: A full circle is 360 degrees (°).
- Radians: A full circle is 2π radians. Radians are often preferred in calculus and higher mathematics because they simplify many formulas.
When using trigonometric functions in calculations, it's crucial to know whether your angle is in degrees or radians and to ensure your calculator or software is set to the correct mode.
Applications of Trigonometry:
Trigonometry has widespread applications in various fields, including:
- Physics: Analyzing waves, oscillations, projectile motion, and forces.
- Engineering: Designing structures, calculating distances, surveying, and navigation.
- Computer Graphics: Creating 2D and 3D graphics, animations, and rendering.
- Astronomy: Measuring distances to stars and planets, understanding celestial movements.
- Music Theory: Analyzing sound waves and harmonies.
This calculator allows you to quickly compute the value of the six basic trigonometric functions for a given angle, whether measured in degrees or radians.
function calculateTrig() {
var angleValueInput = document.getElementById("angleValue");
var angleUnit = document.getElementById("angleUnit").value;
var trigFunction = document.getElementById("trigFunction").value;
var resultValueDisplay = document.getElementById("result-value");
var angleValue = parseFloat(angleValueInput.value);
if (isNaN(angleValue)) {
resultValueDisplay.textContent = "Invalid Input";
return;
}
var angleInRadians;
if (angleUnit === "degrees") {
angleInRadians = angleValue * (Math.PI / 180);
} else {
angleInRadians = angleValue;
}
var result = NaN;
try {
switch (trigFunction) {
case "sin":
result = Math.sin(angleInRadians);
break;
case "cos":
result = Math.cos(angleInRadians);
break;
case "tan":
// Handle vertical asymptotes for tan(x) where cos(x) is 0
if (Math.abs(Math.cos(angleInRadians)) < 1e-10) { // Using a small tolerance for floating point comparison
resultValueDisplay.textContent = "Undefined (approaching infinity)";
return;
}
result = Math.tan(angleInRadians);
break;
case "csc":
// Handle vertical asymptotes for csc(x) where sin(x) is 0
if (Math.abs(Math.sin(angleInRadians)) < 1e-10) {
resultValueDisplay.textContent = "Undefined (approaching infinity)";
return;
}
result = 1 / Math.sin(angleInRadians);
break;
case "sec":
// Handle vertical asymptotes for sec(x) where cos(x) is 0
if (Math.abs(Math.cos(angleInRadians)) < 1e-10) {
resultValueDisplay.textContent = "Undefined (approaching infinity)";
return;
}
result = 1 / Math.cos(angleInRadians);
break;
case "cot":
// Handle vertical asymptotes for cot(x) where sin(x) is 0
if (Math.abs(Math.sin(angleInRadians)) < 1e-10) {
resultValueDisplay.textContent = "Undefined (approaching infinity)";
return;
}
result = 1 / Math.tan(angleInRadians);
break;
default:
resultValueDisplay.textContent = "Select a function";
return;
}
if (isNaN(result)) {
resultValueDisplay.textContent = "Error";
} else {
// Round to a reasonable number of decimal places for display
resultValueDisplay.textContent = result.toFixed(8);
}
} catch (e) {
resultValueDisplay.textContent = "Error calculating";
console.error("Calculation error:", e);
}
}