Sine, Cosine, Tangent Calculator
Instantly find the sine, cosine, and tangent of any angle entered in degrees, radians, or gradians. Useful for geometry homework, engineering calculations, and programming projects.
About this calculator
The three primary trigonometric ratios — sine, cosine, and tangent — are defined on the unit circle and describe the relationship between angles and side ratios in right triangles. For a right triangle with hypotenuse r: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent = sin θ/cos θ. Angles can be measured in degrees (full circle = 360°), radians (full circle = 2π), or gradians (full circle = 400 grad). Conversion formulas: radians = degrees × π/180; gradians = degrees × 200/180. This calculator converts your input to radians before applying the standard math functions, so results are consistent across all three unit systems. Tangent is undefined at 90° (π/2 rad) and 270° because cosine equals zero at those points.
How to use
Find sin, cos, and tan for θ = 45°. Convert to radians: 45 × π/180 ≈ 0.7854 rad. sin(45°) = √2/2 ≈ 0.7071. cos(45°) = √2/2 ≈ 0.7071. tan(45°) = sin/cos = 1.0000. Now try θ = 200 grad (gradians): convert to degrees first — 200 × (360/400) = 180°, so sin(180°) = 0, cos(180°) = −1, tan(180°) = 0. Enter your angle, select the unit, set the desired decimal precision, and the calculator returns all three values simultaneously.
Frequently asked questions
What is the difference between sine, cosine, and tangent?
Sine, cosine, and tangent are the three fundamental trigonometric functions. Sine gives the ratio of the opposite side to the hypotenuse in a right triangle; cosine gives the adjacent side to the hypotenuse; tangent gives the opposite side to the adjacent side. On the unit circle, cos θ is the x-coordinate and sin θ is the y-coordinate of the point at angle θ. Tangent equals sin θ divided by cos θ and represents the slope of the line at that angle.
How do I convert between degrees, radians, and gradians for trig calculations?
To convert degrees to radians, multiply by π/180 (e.g. 90° × π/180 = π/2 ≈ 1.5708 rad). To convert degrees to gradians, multiply by 400/360 = 10/9 (e.g. 90° = 100 grad). To go from radians back to degrees, multiply by 180/π. Gradians, also called gons, divide a full circle into 400 equal parts and are used in surveying and some European engineering disciplines. This calculator accepts all three units, so you never need to convert manually.
Why is tangent undefined at 90 degrees and what happens near that angle?
Tangent is defined as sin θ / cos θ. At exactly 90°, cos θ = 0, making the division undefined — there is no finite value for tan(90°). Geometrically, the angle's terminal side is vertical, meaning the 'adjacent' side of the right triangle has zero length. As θ approaches 90° from below, tan θ grows toward positive infinity; from above 90°, it approaches negative infinity. This discontinuity is called a vertical asymptote and repeats every 180°, at 90°, 270°, 450°, and so on.