The Trigonometric Calculator computes the values of trigonometric functions such as sine (sin), cosine (cos), and tangent (tan), as well as their reciprocal and inverse functions, using three simple inputs. Instead of memorizing trigonometric tables or manually applying formulas, this tool instantly delivers accurate results for any valid angle. It is widely useful in mathematics, physics, engineering, architecture, and computer graphics, where angle-based calculations are frequent. Students, educators, and professionals can use it to check homework, analyze wave functions, solve geometry problems, or perform quick design checks.

Required Inputs & Typical Use Cases

• Angle (θ)

  The measure of the angle you want to evaluate. Enter a numeric value (e.g., 30 or π/4).

• Unit Selector

  Specify whether the angle is given in degrees or radians to ensure accurate results.

• Function Type

  Select which trigonometric function you want to calculate — sine, cosine, tangent, or their reciprocal/inverse functions.

Common scenarios: (1) Calculate sin(30°), cos(π/4), or tan(60°); (2) Convert between degree and radian measures for study or exams; (3) Model oscillations and waveforms in physics and electrical engineering; (4) Solve triangle problems in geometry and trigonometry; (5) Apply trig functions to computer graphics, animations, and signal processing.

The Formula

The core trigonometric functions are defined as:
sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent
Where θ is the angle, and the sides are defined relative to θ in a right triangle.

• θ

  The input angle, measured in degrees or radians

• sin(θ), cos(θ), tan(θ)

  The resulting trigonometric ratio values

• opposite, adjacent, hypotenuse

  The triangle side lengths used in definitions

Worked Example

1. Step 1: Choose inputs

   Suppose you want to calculate sin(30°). Set Function = sine, Angle = 30, and Unit = degrees.

2. Step 2: Apply definition

   Use sin(θ) = opposite / hypotenuse. For a standard 30° angle, the ratio is 1/2.

3. Step 3: Solve

   sin(30°) = 0.5.

4. Result

   The calculator outputs sin(30°) = 0.5.

Tips, Assumptions & Limitations

• Always check whether you are using degrees or radians.
• Remember that tan(90°), cot(0°), and similar cases are undefined.
• Trigonometric values are periodic, repeating every 360° or 2π radians.
• Radians are preferred in physics and calculus for accurate modeling.
• Results for non-standard angles may have long decimals — round where needed.