Trig Degree Calculator

Enter an angle in degrees to get its sine, cosine, and tangent (sin θ, cos θ, tan θ), plus the equivalent angle in radians.

Quick Facts

Sine
sin(θ) = opposite / hypotenuse
Ranges from -1 to 1 for every angle.
Cosine
cos(θ) = adjacent / hypotenuse
Also ranges from -1 to 1; cos(θ) = sin(90° - θ).
Tangent
tan(θ) = sin(θ) / cos(θ)
Undefined at 90°, 270°, and every 180° step from those angles.
Degrees to radians
radians = degrees × π/180
A full circle is 360° = 2π radians.

Your Results

Calculated
Sine — sin(θ)
-
Ratio of opposite to hypotenuse
Cosine — cos(θ)
-
Ratio of adjacent to hypotenuse
Tangent — tan(θ)
-
sin(θ) / cos(θ)
Angle in Radians
-
θ × π/180

Ready

Enter an angle in degrees, then press Calculate.

How the Trig Degree Calculator Works

Sine, cosine, and tangent are ratios defined from a right triangle, and by extension from the unit circle: for an angle θ measured from the positive x-axis, cos(θ) is the x-coordinate and sin(θ) is the y-coordinate of the point where the angle's ray meets a circle of radius 1. This calculator takes an angle in degrees, converts it to radians, and evaluates all three ratios directly with JavaScript's built-in trigonometric functions.

Converting degrees to radians

Degrees and radians are two different units for measuring the same angle. A full turn is 360° or 2π radians, so 1° = π/180 radians ≈ 0.017453 radians. The calculator applies this conversion first — radians = degrees × π/180 — because the underlying Math.sin/Math.cos/Math.tan functions expect radians, not degrees.

Evaluating sine, cosine, and tangent

Once the angle is in radians, sin(θ) and cos(θ) are read directly from the unit circle and always fall between -1 and 1. Tangent is then computed as tan(θ) = sin(θ) / cos(θ), which is also the slope of the angle's ray. Because tangent is a ratio with cos(θ) in the denominator, it is undefined wherever cos(θ) = 0 — that is, at 90°, 270°, and every angle 180° away from those (…, -270°, -90°, 90°, 270°, 450°, …).

Common mistakes

  • Degrees vs. radians: entering an angle meant for radians (e.g., 1.5) as if it were degrees gives a completely different, wrong result. Always confirm the unit before comparing to another source.
  • Expecting a tangent value near 90°: as θ approaches 90° or 270°, tan(θ) grows without bound; the calculator reports "Undefined" exactly at those angles rather than a huge number.
  • Reading sign incorrectly: sin and cos are negative in some quadrants (for example, cos is negative for 90° < θ < 270°) — a negative result is not an error.

Real-world applications

  • Finding missing sides or angles in right triangles (surveying, construction, navigation)
  • Modeling periodic phenomena: sound waves, AC current, tides, and mechanical vibration all follow sinusoidal patterns based on sin/cos of an angle that grows with time
  • Rotational kinematics, robotics, and computer graphics, where converting a heading in degrees into x/y components requires exactly this sin/cos evaluation

Frequently Asked Questions

How do I find the sine, cosine, and tangent of an angle in degrees?
Enter the angle in degrees and press Calculate. The tool converts the angle to radians using radians = degrees × π/180, then evaluates sin(θ), cos(θ), and tan(θ) = sin(θ)/cos(θ).
How do I convert degrees to radians?
Multiply the degree value by π/180 (≈0.017453). For example, 45° × π/180 ≈ 0.7854 radians. A full circle is 360° = 2π radians.
Why is the tangent undefined at 90° and 270°?
Tangent equals sin(θ)/cos(θ), and cos(θ) = 0 at 90°, 270°, and every 180° interval from those angles, which makes the ratio undefined (division by zero). Sine and cosine remain fully defined for every angle.
What are the sine, cosine, and tangent for common angles like 30°, 45°, and 60°?
sin30° = 0.5, cos30° ≈ 0.866, tan30° ≈ 0.577; sin45° = cos45° ≈ 0.7071, tan45° = 1; sin60° ≈ 0.866, cos60° = 0.5, tan60° ≈ 1.732. These come from the 30-60-90 and 45-45-90 special right triangles.

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