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Trigonometric Functions Explained: Unit Circle, Sin, Cos, Tan

Explore the generation of sin, cos, and tan using the unit circle. Study different frequencies in sin and cos functions. Master trigonometry with unlimited exercises, triangle properties, parametric curves, Fourier transformation, supersonic flight, music harmonics, and more.

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Trigonometric Functions Explained: Unit Circle, Sin, Cos, Tan

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  1. Trigonometric functions with unit circle: sin cos tan Here you can study (in slow motion if you want) the generating of sin, cos and tan by the help of the unit circle

  2. Different frequencies in sin and cos functions Here you can quickly study different frequencies in sin and cos functions

  3. Exercises (unlimited) I Here you can generate an unlimited number of triangles measure and/or compute by calculator angles, lines, circumferences and areas and have feedback if your answers are correct or not

  4. Exercises (unlimited) II

  5. Exercises (unlimited) III

  6. Triangel - Properties Here you can study different properties of triangles

  7. Parametric curves 2D I Here you can generate different nice curves by trigonometric functions, measure angles and compute point positions on the curves

  8. Parametric curves 2D II

  9. Parametric curves 2D III

  10. Parametric curves 3D Here you can generate different nice curves by trigonometric functions, measure angles and compute point positions on the curves in space

  11. Fourier Here you can study how we can replace different functions by a sum of sin and cos functions

  12. Fourier and Heat Transfer Here you can study how we can replace different functions by a sum of sin and cos functions and make use of this to find out how heat is transfered through a rod

  13. Sampling Here you can study how we can replace different functions by a sum of sin and cos functions and make use of this to digitize signals (TV, radio, mobilephone, pictures, movies, …)

  14. Supersonic flight Here you can study the connection of the speed of a supersonic flight and the generated shock waves

  15. Music - Beat Here you can play on two pianos at the same time, listen to the music and study what happens when two music tones differ with a small amount of frequencies.

  16. Cycloide - Path of a point on the rim of a circle (x,y) Here you can study the movement of a point at the rim of a rolling wheel. The path is called a cycloide and have many interesting properties. You can also find out the the point of the wheel touching the ground has zero velocity while the point on the top has a velocity twice of the velocity of the centre. So if you drive a car in 80 km/h, a point on the rim change it’s velocity between 0 and 160 km/h.

  17. Light - Polarization Here you can study polarization of light and how our sunglasses can remove reflecting light waves

  18. Simple Harmonic Motion (SHM) Here you can study the movement of the a particle in a simple harmonic motion. This study is important to understand electromagnetic waves (also light) and waves on the sea.

  19. Waves Here you can study the movement of harmonic waves (sin and cos waves)

  20. Music - Harmonics Here you can study harmonic tones on a music instrument. When you play on an instrument, then you generate sin and cos waves with a bacis frequency and multiple frequencies (harmonis tones) of this basic frequency.

  21. Collision Here you can study collisions by measuring positions, velocities and angles using sin and cos functions

  22. House Here you can study change of the height of the house and measure/compute different angles

  23. Measure in SimReal I Different tool for measuring in SimReal

  24. Measure in SimReal II Measure result Special measure tool On / Off Move Measure type Measure-probe Measuring tool in SimReal

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