Register  
 
 About Us | Help | Sign in
 
HomeForumsArticlesRevision NotesPersonal StatementsUniversity GuidesHealth & RelationshipsCareers
Create New Article | Editing Help  
   

Advanced Search
Revision:Sin, Cos and Tan

From The Student Room

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Sin, Cos and Tan


(Diagram of triangle needed)


In any right angled triangle, for any angle:

\displaystyle \mathsf{The\ sine\ of\ the\ angle} = \frac{\mathsf{the\ length\ of\ the\ opposite\ side}}{\mathsf{the\ length\ of\ the\ hypotenuse}}


\displaystyle \mathsf{The\ cosine\ of\ the\ angle} = \frac{\mathsf{the\ length\ of\ the\ adjacent\ side}}{\mathsf{the\ length\ of\ the\ hypotenuse}}


\displaystyle \mathsf{The\ tangent\ of\ the\ angle} = \frac{\mathsf{the\ length\ of\ the\ opposite\ side}}{\mathsf{the\ length\ of\ the\ adjacent\ side}}


The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question.

\displaystyle \sin = \frac{o}{h}

\displaystyle \cos = \frac{a}{h}

\displaystyle \tan = \frac{o}{a}


Often remembered by: soh cah toa.


Example

Find the length of side x in the diagram below:


(diagram for question missing)


The angle is 60 degrees. We are given the hypotenuse and need to find the adjacent side. This formula which connects these three is:

\displaystyle \cos \mathsf{(angle)} = \frac{\mathsf{adjacent}}{\mathsf{hypotenuse}}

therefore, \displaystyle \cos 60 = \frac{x}{13}

therefore, x = 13 \times \cos 60 = 6.5

therefore the length of side x is 6.5cm.


The graphs of sin, cos and tan

The following graphs show the value of \sin\phi, \cos\phi and \tan\phi against \phi (\phi represents an angle).

From the sin graph we can see that \sin\phi = 0 when \phi = 0 degrees, 180 degrees and 360 degrees.


(diagram of graphs missing)



Comments

More is probably needed on the graphs for A and A* grade questions at Higher level GCSE.

This article is far too basic for the understanding of these topics at A Level (C1 module).

A look at contextual problems would be good, or a mentions of areas which are commonly connected with trig in exam questions would be useful.

Retrieved from "http://thestudentroom.co.uk/wiki/Revision:Sin%2C_Cos_and_Tan"
Article Tools:  Create New Article  |  Report This Article  |  This Article's History  | 
collapse
Recent Threads
 
collapse What do people now class as fat?
started by: beckytc90
replies: 43
last post: 1 Minute Ago
collapse Your favourite all time 'retro' sweet/s?
started by: preshalinko3
replies: 29
last post: 1 Minute Ago
collapse WWIII - what would you do? (Poll)
started by: AWZC
replies: 87
last post: 1 Minute Ago
collapse What was the name of thsi film?
started by: Reagan Smash
forum: Film
replies: 5
last post: 1 Minute Ago
collapse Is Art a "doss subject"?
replies: 112
last post: 1 Minute Ago