Trigonometry Calculator
Enter an angle to find its sine, cosine, tangent, and reciprocal functions. The calculator also shows the equivalent angle in both units, its quadrant and reference angle, and its position on the unit circle.
Trigonometric results
0.70710678
0.70710678
1
1.41421356
1.41421356
1
Angle conversion
Degrees
45°
Radians
0.78539816 rad
Normalized angle
45°
Angle properties
Quadrant
Quadrant I
Reference angle
45°
Sign rule
All functions are positive
Unit circle
The point on the unit circle is (cos θ, sin θ).
X coordinate (cos θ)
0.70710678
Y coordinate (sin θ)
0.70710678
Radius
1
What the values mean
On the unit circle, an angle θ corresponds to the point (cos θ, sin θ). Sine is the point's vertical coordinate and cosine is its horizontal coordinate. Tangent is sin θ divided by cos θ, when cos θ is not zero. In a right triangle, these same ratios are commonly described as opposite over hypotenuse, adjacent over hypotenuse, and opposite over adjacent.
The reciprocal functions are cosecant (1 ÷ sin θ), secant (1 ÷ cos θ), and cotangent (cos θ ÷ sin θ). A reciprocal is undefined when its denominator is zero, so some values are undefined at particular angles rather than being ordinary numbers.
Degrees and radians
A full turn is 360° or 2π radians, so 180° equals π radians. To convert degrees to radians, multiply by π ÷ 180; to convert radians to degrees, multiply by 180 ÷ π. For example, 45° equals π ÷ 4 radians, and sin 45° = cos 45° = √2 ÷ 2 while tan 45° = 1.
Choose the unit that matches your input. The calculator accepts negative angles and angles beyond one full rotation; its normalized angle shows the equivalent position from 0° up to (but not including) 360°.
When tangent is undefined
Tangent is undefined wherever cosine is zero, including 90° and 270° (and equivalent angles one or more full turns away). At these positions, dividing sine by cosine would require division by zero. The calculator reports undefined values instead of displaying an infinite or misleading number.
Results are rounded to the selected display precision. Rounding affects only how a value is shown; it does not change the underlying trigonometric calculation.