Trigonometry

But really similarity

All the things I have to teach and the kids can’t remember – a few I heard back from

Graphing trig functions

Special triangles

Proving identities

Double/half angle; sum of angles formulas

Things I wonder how we teachThings I wonder how we teach Special triangles

Graphing sine and cosine

Trig identities – cosine of the sum of two angles,

Law of sines, law of cosines,

The trigonometry started with the study f h d h i th i ?of chords – where is the sine?

Unit circle:

The word sine:The word sine: The Sanskrit word for chord-half was jya-ardha, which was

sometimes shortened to jiva.This was brought into Arabic as jiba, and written in Arabic simply with two consonants jb,vowels not being written Later Latin translators selected the vowels not being written. Later, Latin translators selected the word sinus to translate jb thinking that the word was an arabicword jaib, which meant breast, and sinus had breast and bay as two of its meanings. In English, sinus was imported as "sine".

The word cosine?

Similar trianglesgc d e

fj

kl

bg

ik

bh

oam

o

n

)4363sin( olhfb )43.63sin( mjgda

An interesting problem!?An interesting problem!? Find the rational value of

80tan70tan60tan50tan40tan30tan20tan10tan

Where are these functions?Where are these functions?

H ld th g h f( ) i ( )How would you then graph f(x)=sin(x)

Are trig functions useful with area ti ?questions?

Find areas of both triangles AMC and BMC

C

A

M B

Let’s look at this pictureLet’s look at this picture

And the finalAnd the final

Law of cosinesLaw of cosines

Law of cosines 2Law of cosines 2

Cyclic quadrilateralsCyclic quadrilaterals

Ptolemy’s theoremy

Why would we need it? Why would we need it?