Degree system

radians

An angle is 90 degrees

The sum of the other two angles is 90 degrees

Ratio of opposite side to hypotenuse

Ratio of adjacent side to hypotenuse

The ratio of the opposite side to the adjacent side

coordinates of intersection

tangent

The period is 360 degrees or 2π radians

Period is 180 degrees or π radians

odd function

even function

odd function

1, 1

all real numbers

cyclical fluctuations

Amplitude is 1

cyclical fluctuations

Amplitude is 1

The phase ratio sine function image is shifted 90 degrees to the left

Increases from negative infinity to positive infinity in each period

Period is π radians

Sound waves, light waves, etc.

Simple harmonic motion etc.

Filter design, etc.

Calculation of stress and strain, etc.

Prediction of star motion, etc.

Phase difference between voltage and current, etc.

3D modeling and rendering, etc.

Fast Fourier Transform, etc.

Inverse function of sine function

Inverse function of cosine function

inverse function of tangent function

A type of hyperbolic trigonometric function

A type of hyperbolic trigonometric function

A type of hyperbolic trigonometric function

Euler's formula

Conversion between exponential and trigonometric forms of complex numbers

Irrational numbers were discovered

Discussion of angles in "Elements"

Early studies of trigonometric functions

Compilation of trigonometric function tables

Systematic study of trigonometry

The creation of analytic geometry

The combination of trigonometric functions and coordinate systems

Based on the concepts of limits and infinitesimal quantities

Calculus

complex analysis

Fourier analysis