Graphs of trigonometric functions

Basic Trigonometric Functions

Sine (sin), cosine (cos), and tangent (tan) are fundamental trigonometric functions.
These functions represent the ratio of sides in a right-angled triangle.

All trigonometric functions are periodic, meaning they repeat their values in regular intervals or periods.
The sine and cosine functions are periodic with a period of 2π, while the tangent function is periodic with a period of π.

The graph of sin(x) starts at the origin (0,0), reaches its peak at π/2, comes back to 0 at π, goes to its lowest at 3π/2, and returns to 0 at 2π, repeating the pattern thereafter.
The graph of cos(x) starts from a peak at (0,1), moves to 0 at π/2, reaches its lowest point at π, goes back to zero at 3π/2, reaches a peak at 2π, and continues repeating the pattern.

The graph of tan(x) is different from sin(x) and cos(x). It starts from zero, increases indefinitely, approaches vertical asymptotes at ±π/2, becomes undefined at these points, decreases from there, reaches zero at π, and repeats the pattern.
Unlike sin and cos, tan has a period of π instead of 2π.

Amplitude change: The graphs of sin and cos can change amplitude (height) with a multiplier called the amplitude factor. For instance, in f(x) = Asin(x) or f(x) = Acos(x), the amplitude is A .
Frequency change: A horizontal compression or stretch in the graph by a factor B creates a frequency change, as seen in f(x) = sin(Bx) or f(x) = cos(Bx).
Phase shift or horizontal shift: This is a movement of the entire graph horizontally. It’s introduced by a constant added or subtracted from x, as in f(x) = sin(x + C).
Vertical shift: This is a movement of the entire graph up or down and is introduced by a constant added or subtracted from the entire function, as in f(x) = sin(x) + D.

Inverse trigonometric functions, such as arcsin or sin^-1, arccos or cos^-1, and arctan or tan^-1 are used to reverse sine, cosine, and tangent.
These functions allow you to input a ratio and get an angle that would give you that ratio.