# Sketch and Use Graphs y=sin x, y=cos x, y=tan x

## Sketch and Use Graphs y=sin x, y=cos x, y=tan x

**Understanding the Graphs**

- The graphs
**y = sin x**,**y = cos x**, and**y = tan x**are the visual representations of the sine, cosine, and tangent functions respectively, for all values of x. - These functions are repetitive, which means they cycle over a set period. This property makes them
**periodic functions**. - The
**period**for both**y = sin x**and**y = cos x**is**2π**(or 360°), while for**y = tan x**it is**π**(or 180°).

**Sketching the Sine Graph (y = sin x)**

- The sine graph starts at (0,0), goes to (π/2,1), then to (π,0), (3π/2,-1), and finally to (2π,0) before repeating the cycle.
- The maximum height and depth the sin graph reaches are 1 and -1 respectively.

**Sketching the Cosine Graph (y = cos x)**

- The cosine graph starts at (0,1), goes to (π/2,0), then to (π,-1), (3π/2,0), and finally to (2π,1) before repeating.
- The maximum height and depth the cos graph reaches are 1 and -1 respectively.

**Sketching the Tangent Graph (y = tan x)**

- The graph of tangent has vertical asymptotes at odd multiples of π/2 (±π/2, ±3π/2, ±5π/2, etc.) as tan x approaches positive or negative infinity.
- At multiples of π, tan x is 0.

**Using the Graphs**

- Periodic nature of these functions makes them useful in modelling phenomena that repeat over time like sound or light waves.
- The
**y = sin x**and**y = cos x**graphs are used to represent oscillations, waveforms, or any periodic motion. - The
**y = tan x**graph, due to its unique shape and properties, is often used in engineering and physics to model certain types of non-repeating phenomena.

**Remember:**

- The graphs of these functions are useful not just in geometry, but in a variety of fields including physics, engineering, music, biology, and even finance.
- Understanding the shape, values, and properties of these graphs is key to mastering the trigonometric functions and their applications.