Calculate trigonometric functions and conversions instantly by entering an angle in degrees.
Radians (rad)
0
Sine (sin)
0
Cosine (cos)
0
Tangent (tan)
0
Secant (sec)
0
Cosecant (csc)
0
Understanding Degrees in Trigonometry
In mathematics, degrees are a measurement of plane angles, represented by the symbol °. A full rotation is defined as 360 degrees. While radians are often used in calculus, degrees remain the standard in navigation, engineering, and basic geometry due to their historical significance and ease of use in dividing circles into segments.
How to Calculate Trigonometric Functions from Degrees
Most programming languages and scientific libraries perform trigonometric calculations in radians. To use a "calculator in degrees," the first step is converting the input. The fundamental conversion formula is:
Radians = Degrees × (π / 180)
Once you have the value in radians, you can determine the primary ratios:
Sine (sin): The ratio of the opposite side to the hypotenuse.
Cosine (cos): The ratio of the adjacent side to the hypotenuse.
Tangent (tan): The ratio of the opposite side to the adjacent side (sin/cos).
Common Angle Reference Table
Degrees
Radians
Sine
Cosine
0°
0
0
1
30°
π/6
0.5
0.866
45°
π/4
0.707
0.707
60°
π/3
0.866
0.5
90°
π/2
1
0
Practical Applications
Using a degree-based calculator is essential in several fields:
Architecture: Determining roof pitches and structural angles.
Physics: Calculating projectile motion and vector components.
Astronomy: Measuring the positions of celestial bodies across the sky.
Gaming: Calculating rotation and movement vectors in 2D and 3D environments.
function calculateTrigValues() {
var degreeVal = document.getElementById("degreeInput").value;
if (degreeVal === "" || isNaN(degreeVal)) {
alert("Please enter a valid number for degrees.");
return;
}
var degrees = parseFloat(degreeVal);
var radians = degrees * (Math.PI / 180);
var sinVal = Math.sin(radians);
var cosVal = Math.cos(radians);
var tanVal = Math.tan(radians);
// Handle undefined cases for Tan, Sec, Csc
var displayTan = (Math.abs(cosVal) < 1e-10) ? "Undefined" : tanVal.toFixed(4);
var displaySec = (Math.abs(cosVal) < 1e-10) ? "Undefined" : (1 / cosVal).toFixed(4);
var displayCsc = (Math.abs(sinVal) < 1e-10) ? "Undefined" : (1 / sinVal).toFixed(4);
// Update UI
document.getElementById("resRad").innerHTML = radians.toFixed(4);
document.getElementById("resSin").innerHTML = sinVal.toFixed(4);
document.getElementById("resCos").innerHTML = cosVal.toFixed(4);
document.getElementById("resTan").innerHTML = displayTan;
document.getElementById("resSec").innerHTML = displaySec;
document.getElementById("resCsc").innerHTML = displayCsc;
// Show results
document.getElementById("resultsArea").style.display = "grid";
}