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Trigonometric Identities Calculator

From one known function value and a quadrant, rebuild all six functions with the right signs, then check the Pythagorean, reciprocal, double-angle and half-angle identities.

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Open Trigonometric Identities Calculator and you get an answer straight away, with no account to create. You will find it under Trigonometry, with Trigonometric Equation Solver and Trigonometric Function Grapher for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Trigonometric Identities Calculator?

From one known function value and a quadrant, rebuild all six functions with the right signs, then check the Pythagorean, reciprocal, double-angle and half-angle identities.

When would I actually use this?

Solving a triangle from what you can actually measure, converting between degrees and radians, and checking an identity before using it.

What is the most common mistake?

Leaving the calculator in the wrong angle mode. Degrees and radians differ by a factor of about 57, and the answer is wrong without ever looking wrong.

How is Trigonometric Identities Calculator different from Trigonometric Equation Solver?

They sit next to each other but answer different questions: Trigonometric Equation Solver is the one to open when you need it to solve sin, cos and tan equations on any interval by robust numerical root-finding — results as multiples of π, radians and degrees, with interval presets for [0,2π], [−π,π], [0,4π] and [0°,360°]. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Trigonometric Function Grapher is the closest one after this: Plot A·f(Bx − C) + D for sin, cos, tan, cot, sec and csc with the asymptotes drawn, plus amplitude, period, phase shift, midline, domain, range and key points.

What else is worth having open alongside it?

Arccos Calculator and Arcsin Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The identities are the classical ones and the arithmetic is exact to double precision. The law-of-sines case with two sides and a non-included angle can have two valid triangles, and both are reported.

Further reading

All guides →
ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerFibonacci and the Golden RatioThe Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.
Trigonometric Identities Calculator — OneKitly