Sin, cos, tan

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Tutor: Bilal

Summary

Sin, cos, tan

In a nutshell

sin()\sin()​​, cos()\cos()​, and tan()\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

xx​​

The angle you're focusing on (you will either have to find out the value of xx​ or use it to find the length of a side)

Hypotenuse

The longest side of the triangle

Opposite

The side opposite the angle labelled xx​​

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()​​

sin(x)=oppositehypotenuse\sin(x)=\frac{opposite}{hypotenuse}​​

SOH

Cosine

cos()\cos()​​

cos(x)=adjacenthypotenuse\cos(x)=\frac{adjacent}{hypotenuse}​​

CAH

Tangent

tan()\tan()​​

tan(x)=oppositeadjacent\tan(x)=\frac{opposite}{adjacent}​​

TOA


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




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