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Trigonometric Functions Calculator

Calculate all six trigonometric functions (sin, cos, tan, csc, sec, cot) for any angle.

Reviewed by Chase FloiedUpdated

This free online trigonometric functions calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Results

sin(θ)

0.707107

cos(θ)

0.707107

tan(θ)

1

csc(θ)

1.414214

sec(θ)

1.414214

cot(θ)

1

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Trigonometric Functions Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Trigonometric Functions Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

Trigonometric Functions Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • •Use the Trigonometric Functions Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The Trigonometric Functions Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Calculate all six trigonometric functions (sin, cos, tan, csc, sec, cot) for any angle. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About Trigonometric Functions Calculator

The six trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — form the foundation of trigonometry. They relate angles to ratios of sides in right triangles and extend to all real numbers via the unit circle. Sine and cosine are the primary functions; the other four are derived from them. These functions are periodic, meaning they repeat their values at regular intervals: sin and cos have period 360° (2π), while tan and cot have period 180° (π). Trigonometric functions are essential in physics (wave motion, oscillation, rotation), engineering (signal processing, AC circuits), computer science (graphics, animation), and music (sound waves). This calculator evaluates all six functions simultaneously for any angle.

The Math Behind It

In a right triangle, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent. The reciprocals are csc θ = 1/sin θ, sec θ = 1/cos θ, and cot θ = 1/tan θ. The Pythagorean identities connect them: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, and 1 + cot²θ = csc²θ. The functions have specific domains and ranges: sin and cos are defined everywhere with range [−1, 1]; tan and sec are undefined where cos θ = 0; csc and cot are undefined where sin θ = 0. The Taylor series expansions are sin x = x − x³/3! + x⁵/5! − ... and cos x = 1 − x²/2! + x⁴/4! − ..., converging for all real x. Euler's formula e^(ix) = cos x + i sin x unifies trigonometric and exponential functions. The Fourier theorem states that any periodic function can be decomposed into a sum of sines and cosines, which is the basis of spectral analysis and signal processing.

Formula Reference

Primary Functions

sin θ, cos θ, tan θ = sin θ / cos θ

Variables: θ = angle

Reciprocal Functions

csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ

Variables: θ = angle

Worked Examples

Example 1: All six functions at 60°

Compute all six trig functions at θ = 60°.

Step 1:sin(60°) = √3/2 ≈ 0.8660
Step 2:cos(60°) = 1/2 = 0.5
Step 3:tan(60°) = √3 ≈ 1.7321
Step 4:csc(60°) = 2/√3 ≈ 1.1547
Step 5:sec(60°) = 2
Step 6:cot(60°) = 1/√3 ≈ 0.5774

All six values computed from the 30-60-90 triangle ratios.

Common Mistakes & Tips

  • !Confusing degrees and radians — always check your calculator mode.
  • !Forgetting that tangent and secant are undefined at 90°, 270°, etc.
  • !Mixing up reciprocal pairs: csc goes with sin, sec goes with cos, cot goes with tan.

Related Concepts

Unit Circle

Geometric interpretation of all trig functions.

Arcsin Calculator

Find angles from sine values.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Double Angle Formula Calculator

Hypotenuse Calculator

Unit Circle Calculator

Frequently Asked Questions

What is the difference between sin and csc?

csc(θ) = 1/sin(θ). They are reciprocals of each other.

Which trig functions can have values greater than 1?

tan, cot, csc, and sec can all have absolute values greater than 1. Only sin and cos are bounded between −1 and 1.