**Instructions:**

- Enter an angle in radians (π) in the input field above.
- Click the "Calculate" button to calculate the trigonometric functions.
- The results for sin(π), cos(π), tan(π), csc(π), sec(π), and cot(π) will be displayed below.
- You can copy the results by clicking the "Copy Results" button.
- The calculation history will be displayed in the "Calculation History" section below the results.
- Use this tool to explore various trigonometric calculations!

**Results**

**Calculation History**

The trigonometric functions calculator ƒ(π) is a useful mathematical tool for evaluating sine, cosine, tangent and their inverse functions at different multiples of π. It allows exploring trigonometry concepts visually using the unique properties of pi.

## Concept

The calculator generates values of trig functions at:

0, π/6, π/4, π/3, π/2, 2π/3, 3π/4, 5π/6, π, 7π/6, etc.

It implements the trigonometric circle definitions:

sin θ = y-coordinate on unit circle cos θ = x-coordinate on unit circle tan θ = sin θ / cos θ

Plotting the functional values around the trig circle provides insights into periodicity and symmetry.

## Features

Key features of the ƒ(π) calculator:

- Calculates sin, cos, tan values at pi multiples
- Computes inverse trig functions too
- Generates a table of results
- Interactive trigonometric circle visualization
- Graphs function values around circle
- Illustrates periodic patterns
- Demonstrates symmetry
- Explains connections to unit circle

## Benefits

Benefits of using the ƒ(π) calculator:

- Visualize trig concepts using pi multiples
- Develop intuition for sinusoidal patterns
- Understand symmetry and periodicity
- Learn trig ratios at special angles like π/3, π/4
- Explore inverse trig functions
- Interactive learning tool for trigonometry
- Aid for grasping Visualize trig functions

## Applications

Typical applications include:

- Learning trigonometric concepts
- Studying trig graphs and identities
- Modeling periodic waveforms
- Understanding sine and cosine series
- Solving triangles and trig equations
- Preparing for trigonometry exams

## Conclusion

The ƒ(π) calculator provides an interactive way to develop deeper insights into trigonometric functions using the unique properties of pi. Generating function values at pi multiples and mapping them around the trig circle makes patterns and symmetries more intuitive. It is a useful visualization aid for learning trig concepts.

## References

- Larson, R., & Edwards, B. H. (2013). Calculus (10th ed.). Boston, MA: Brooks Cole.
- Chow, P. (2014). Trigonometry Demystified 2/E (2nd ed.). New York, NY: McGraw-Hill Education.