Sin, cos, tan

In a nutshell

$\sin()$ , $\cos()$ , and $\tan()$ are the three main trigonometric functions and serve as the basis of trigonometry. Using the labels in a right-angled triangle, one can define these functions and their corresponding ratios.

Labelling a triangle

Label	Meaning
$x$	The angle you're focusing on (you will either have to find out the value of $x$ or use it to find the length of a side)
Hypotenuse	The longest side of the triangle
Opposite	The side opposite the angle labelled $x$
Adjacent	The side next to the labelled angle that isn't the hypotenuse

Maths; Trigonometry; KS4 Year 10; Sin, cos, tan

The three trigonometric functions

These are the three main functions and their ratios:

Function name	Found on your calculator as	Corresponding ratio	Simplified version
Sine	$\sin()$	$\sin(x)=\frac{opposite}{hypotenuse}$	SOH
Cosine	$\cos()$	$\cos(x)=\frac{adjacent}{hypotenuse}$	CAH
Tangent	$\tan()$	$\tan(x)=\frac{opposite}{adjacent}$	TOA

Note: It is common and easy to just remember these three ratios as SOHCAHTOA.