Calculate sin, cos, tan, csc, sec, and cot of any angle. Shows quadrant analysis, ASTC rule, Pythagorean identity check, full 0°–360° reference table, and exact values.
The **Sin Cos Tan Calculator** computes all six trigonometric functions — sin(θ), cos(θ), tan(θ), csc(θ), sec(θ), and cot(θ) — simultaneously for any angle entered in degrees, radians, or gradians. It is the most complete single-angle trig tool you will find online, designed for students, teachers, and professionals who need to see every trig value at a glance.
Trigonometric functions are the foundation of angle measurement and periodic analysis. Sine, cosine, and tangent are the three primary functions, defined as ratios of sides in a right triangle (opposite/hypotenuse, adjacent/hypotenuse, and opposite/adjacent, respectively). Their reciprocals — cosecant, secant, and cotangent — complete the set of six. Together, these functions describe the coordinates and slopes of points on the unit circle and appear everywhere from architecture and navigation to signal processing and quantum mechanics.
This calculator highlights the quadrant of your angle using the ASTC mnemonic ("All Students Take Calculus"), which reminds you which functions are positive in each quadrant. It computes the reference angle, verifies the three Pythagorean identities (sin² + cos² = 1, 1 + tan² = sec², 1 + cot² = csc²), and displays bar-chart comparisons of sin, cos, and tan values. A comprehensive reference table covers all 17 standard angles from 0° through 360° with both exact and decimal values. Ten preset buttons provide one-click access to the most commonly needed angles, and a collapsible identities panel lists Pythagorean, reciprocal, cofunction, even/odd, and double-angle identities for quick reference.
Sin Cos Tan Calculator — All 6 Trig Functions helps you avoid repetitive setup mistakes when solving trigonometric and coordinate-geometry problems. Instead of recalculating conversions, signs, and edge cases by hand, you can test inputs immediately, inspect intermediate values, and confirm final answers before submitting work or using numbers in downstream calculations. It surfaces key outputs like sin(θ), cos(θ), tan(θ) in one pass.
The six trig functions relate the sides of a right triangle to its angles. sin = opp/hyp, cos = adj/hyp, tan = opp/adj. Reciprocals: csc = 1/sin, sec = 1/cos, cot = 1/tan. Fundamental identity: sin² + cos² = 1.
Result: sin = √2/2, cos = √2/2, tan = 1
Using θ=45°, the calculator returns sin = √2/2, cos = √2/2, tan = 1. This example mirrors the calculator's live computation flow and is useful for checking manual steps and unit handling.
This calculator is tailored to sin cos tan calculator — all 6 trig functions workflows, including common input modes, unit handling, and special-case behavior. It is designed for fast checking during homework, exam preparation, technical drafting, and coding tasks where trigonometric consistency matters.
Use the primary result together with supporting outputs to verify direction, magnitude, and validity. Cross-check against known identities or geometric constraints, and confirm that angle ranges, sign conventions, and domain restrictions are satisfied before using the numbers elsewhere.
A reliable way to improve is to solve once manually, then verify with the calculator and explain any mismatch. Repeat this on varied examples and edge cases. The built-in preset scenarios for quick trials, comparison tables for side-by-side validation, visual cues that make trends and quadrants easier to read help you build pattern recognition and reduce sign or conversion errors over time.
Sine, cosine, and tangent are the three primary trigonometric functions. In a right triangle with angle θ: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent.
They are the reciprocals of sin, cos, and tan respectively: csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), cot(θ) = 1/tan(θ). They complete the six-function system of trigonometry.
ASTC (All Students Take Calculus) is a mnemonic to remember which trig functions are positive in each quadrant: All in Q1, Sin in Q2, Tan in Q3, Cos in Q4. Use this as a practical reminder before finalizing the result.
sin²(θ) + cos²(θ) = 1, 1 + tan²(θ) = sec²(θ), and 1 + cot²(θ) = csc²(θ). The first is the most fundamental; the others are derived by dividing by cos² or sin².
tan and sec are undefined when cos(θ) = 0 (at 90°, 270°, ...). cot and csc are undefined when sin(θ) = 0 (at 0°, 180°, 360°, ...). This is because they involve division by these values.
The reference angle is the positive acute angle formed between the terminal side of your angle and the nearest part of the x-axis. It always lies in [0°, 90°] and has the same trig absolute values as the original angle.