ARAB CONTR. TO TRIGONOMETRY Flashcards
(21 cards)
TRIGONON
triangle
METRON
measure
Reeasons for interest
- To find prayer time
- location of mecca
help understand movement of planets
Spherical trigonometry
study of celestial sphere- abstract sphere of large radius where planets and stars appear to be fixed
Importance for muslims
- Find dirn. of Qibla
2.prayer imte - distance bw cities
ptolemy- only trig func.
chord
who introduced versine and replaced chord with sine
indians
versin(x) = 1-cosx
who intorduced shadow (umbra) and described sin and cos
& introduced cot
Al Marwazi - 9th century
Where did Al Marwazi compile his results
Book of bodies and distances
who wrote exhaustive treatise on shadows
Al Biruni
tan^2a +1 = sec^2a
tana= sina/cosa
established trig. indentities –> sin(a+b) , sin(a-b)
and spherical sine law
Al Buzjani
2cos(a)cos(b) = cos(a+b) + cos(a-b)
Al Misri - 11th century
importance of trig. tables
to write down tabular info. on how to connect circular motion of circle and the corresponding linear motion on the axis x&y
porduced sine and cosine tables
Al Khwariizmi- 9th century
1st table of shadow function
Al Marwazi - 9th cent.
made table for tan and cot using cota = tan (90-a)
Al biruni
sine table accurate upto 8 decimal places
Al bUzjani
1st to consider trigo. apart from astronomy
Al Tusi
who and which book - introduced concept of polar triangle and developed spherical trig. into present form
Al Tusi - complete quadrilateral
On the sector
Al Tusi
- listed 6 cases of right angle triangle trig.
- stated sine laws for plane and spherical triangles
- discovered law of tangent for spherical triangles and provided its proof
provided 1st statement for law of cosines
Al Kashi
a^2 = b^2+c^2 -2bcos(alpha)
