Trigonometry

Trigonometric Functions

Calculate sin, cos, tan, etc. Free online Trigonometric Functions. Calculate trigonometric functions online — fast, accurate, mobile-friendly, no signup needed.

sin
0.5
cos
0.866025
tan
0.57735

Derivation

  1. ├── 01Givena = 30
  2. ├── 02Formulasin: Qs(t)
  3. ├── 03Compute sin0.5
  4. ├── 04Formulacos: Js(t)
  5. ├── 05Compute cos0.866025
  6. ├── 06Formulatan: a=t,tan(a × π / 180);var a
  7. ├── 07Substitute30=t,tan(30 × π / 180);var 30
  8. └── 08Compute tan0.57735
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§01What is

Understanding the Trigonometric Functions

The Trigonometric Functions computes sin from 1 input: angle (degrees). Calculate sin, cos, tan, etc.

Trigonometry is how we turn angles into distances and distances into angles. It sits under every GPS fix, surveyor measurement, and game-engine render — and it still shows up in carpentry, roof pitches, and woodworking. The Trigonometric Functions sits in that toolkit — it calculate sin, cos, tan, etc. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

sin = Qs(t) | cos = Js(t) | tan = a=t,tan(a × π / 180);var a

Where

a
Angle (degrees)
sin
Output value
cos
Output value
tan
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Angle (degrees) = 30.

  1. 01Start by noting the input — Angle (degrees): 30.
  2. 02Substitute these values into the formula: sin = Qs(t) | cos = Js(t) | tan = a=t,tan(a × π / 180);var a
  3. 03Compute sin: the calculator returns 0.5.
  4. 04Compute cos: the calculator returns 0.866025.
  5. 05Compute tan: the calculator returns 0.57735.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Trigonometric Functions Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Angle (degrees) halved

a = 15 (from 30)

Keep every other input at its default and halve the angle (degrees). See how sin responds.

  1. 01New Angle (degrees): 15
  2. 02Baseline sin: 0.5
  3. 03New sin: 0.258819
  4. 04sin decreases by 48.2% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Angle (degrees) doubled

a = 60 (from 30)

Keep every other input at its default and double the angle (degrees). See how sin responds.

  1. 01New Angle (degrees): 60
  2. 02Baseline sin: 0.5
  3. 03New sin: 0.866025
  4. 04sin increases by 73.2% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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