# Trigonometric Graphs

## Trigonometric Graphs

**Section 1: Basic Understanding**

- Trigonometric graphs are visuals that represent the
**sine**,**cosine**, and**tangent**functions. - The
**x-axis**represents the angle in radians or degrees, while the**y-axis**represents the value of the trigonometric function. - The graphs oscillate between a maximum and a minimum, usually between -1 and 1 for both sine and cosine.

**Section 2: Sine and Cosine Graphs**

- The
**sine graph**starts at 0, rises to 1 at 90 degrees (π/4 rad), falls to 0 at 180 degrees (π rad), decreases to -1 at 270 degrees (3π/4 rad) and returns to 0 at 360 degrees (2π rad). - The
**cosine graph**starts at 1, drops to 0 at 90 degrees (π/4 rad), falls to -1 at 180 degrees (π rad), rises to 0 at 270 degrees (¾π rad) and returns to 1 at 360 degrees (2π rad). - Sine and cosine graphs
**repeat every 360 degrees**(2π rad), which makes them**periodic functions**.

**Section 3: Tangent Graph**

- The
**tangent graph**starts at 0, rises to a value, decreases, and rises again. - Tangent has vertical
**asymptotes**at ±90 degrees and every 180 degrees thereafter. - The tangent graph is also periodic, but it repeats every 180 degrees (π rad).

**Section 4: Transformations of Trigonometric Graphs**

- Trigonometric functions can be transformed by changing their amplitude, period, phase shift, or vertical shift.
**Amplitude**is the ‘height’ of the graph, and a change in amplitude stretches or squashes the graph vertically.**Period**is the ‘length’ of one complete cycle of the graph; altering the period compresses or stretches the graph horizontally.**Phase shift**or horizontal shift moves the graph left or right.**Vertical shift**moves the graph up or down.

**Section 5: Inverse Trigonometric Graphs**

**Inverse trigonometric functions**, such as arcsin (sin^-1), arccos (cos^-1), and arctan (tan^-1), have graphs which are reflections of the original functions in the line y = x.- Inverse trigonometric functions are useful in determining an angle given the sides of a right triangle, and their graphs exhibit the related values of the angles.