Deriving Trig Formulae (Look Ups) by Alexander Forrest
English | November 24, 2022 | ISBN: N/A | ASIN: B0BNCBMPHV | 103 pages | MOBI | 4.97 Mb
Ever wondered how common trig formulae came about ?
This ebook starts with basic trigonometric ratios sineα , cosine α and tangent α
After proving the trig identity sin^2 α +cos^2 α = 1 , it goes on to prove
Formulae for all four quadrants
sin( 90-α ) sin( 180-α ) sin(180+ α ) sin(-α )
cos( 90-α ) cos( 180-α ) cos(180+ α ) cos(-α )
tan( 90-α ) tan( 180-α ) tan(180+ α ) tan(-α )
The relationship between sine, cosine and tangent
Addition Formulae
sin( α + β ) sin( α - β )
cos( α + β ) cos( α - β )
tan( α + β ) tan( α - β )
Double Angle Formulae
sin(2α ) cos(2α) tan(2α)
Half-Angle Formulae
sin(α/2 ) cos(α/2) tan(α/2)
Multiple angles formulae
sin(3α ) cos(3α) tan(3α)
sin(4α ) cos(4α) tan(4α)
sin(5α ) cos(5α) tan(5α)
Products
sinαsinβ cosαcosβ sinαcosβ
Sums and Differences
sinα+sinβ sinα-sinβ
cosα+cosβ cosα-cosβ
This is aimed at AS, A-Level, SQA Higher and SQA Advanced Higher pupils, but is also useful as a refresher for 1st year university level maths .
Ideal as a reference for setting questions or checking answers in a home-schooling environment.
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