Sine Cosine Tangent Calculator
Evaluates all six trigonometric functions—sin, cos, tan, csc, sec, and cot—for any angle in degrees, radians, or gradians. Use it for geometry problems, physics equations, and engineering calculations requiring precise trig values.
About this calculator
The six trigonometric functions relate the angles of a right triangle to the ratios of its sides, and extend naturally to any angle via the unit circle. The primary three are: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent = sin(θ)/cos(θ). The reciprocal functions are: cosecant csc(θ) = 1/sin(θ), secant sec(θ) = 1/cos(θ), cotangent cot(θ) = 1/tan(θ). All computations use radians internally; degrees are converted via rad = θ × π/180, and gradians via rad = θ × π/200. Tangent and cotangent are undefined at angles where their denominators equal zero (e.g. tan(90°) is undefined). The precision field controls rounding to a chosen number of decimal places using the formula: round(result × 10^p) / 10^p, where p is the desired precision.
How to use
Find tan(45°) to 4 decimal places. Step 1 — convert to radians: 45 × π/180 = π/4 ≈ 0.7854 rad. Step 2 — apply the tangent function: tan(π/4) = sin(π/4)/cos(π/4) = (√2/2)/(√2/2) = 1.0000. Step 3 — round to 4 decimal places: round(1.0000 × 10⁴) / 10⁴ = 1.0000. Now try sec(60°): convert 60° to π/3 rad, cos(π/3) = 0.5, so sec(60°) = 1/0.5 = 2.0000. Both results confirm the known exact values for these standard angles.
Frequently asked questions
What is the difference between degrees, radians, and gradians for measuring angles?
Degrees divide a full circle into 360 equal parts and are the most familiar unit in everyday life. Radians measure angles as the ratio of arc length to radius; a full circle is 2π radians (≈6.2832). Radians are the natural mathematical unit and are required by calculus and most physics formulas. Gradians (also called gon or gradian) divide a full circle into 400 equal parts, making a right angle exactly 100 gradians; they were designed for surveying and are common in some European engineering contexts. To convert: degrees × π/180 = radians; degrees × 10/9 = gradians.
Why is tangent undefined at 90 degrees and what happens to the calculator result?
Tangent is defined as sin(θ)/cos(θ). At 90° (π/2 rad), cos(θ) = 0, so the division produces an infinitely large value—the tangent function has a vertical asymptote there. In floating-point arithmetic, cos(π/2) is not exactly zero due to rounding, so a calculator may return a very large number (like 1.633 × 10¹⁶) rather than an error. Similarly, csc is undefined at 0° and 180°, and cot is undefined at 0° and 180°. If you see an extremely large number for these angles, it indicates mathematical undefined behaviour rather than a real result.
How do inverse trigonometric functions differ from the standard ones in this calculator?
Standard trig functions take an angle as input and return a dimensionless ratio. Inverse trig functions (arcsin, arccos, arctan) do the reverse: they take a ratio as input and return an angle. For example, if sin(θ) = 0.5, then arcsin(0.5) = 30°. This calculator computes only the forward (standard) functions. For inverse calculations you would need an arcsin/arccos/arctan tool. The inverse functions are multivalued—sin(30°) and sin(150°) are both 0.5—so by convention arcsin always returns the principal value in the range −90° to +90°.