Trigonometry
Trigonometry αိုαာ ααိαံαဲα αα္αိုα္ေαာ αα်ၤာαာαာαα္αိုα ေααုα် α‘αိααΈါα္αြα့္αို ႏိုα္αါαα္။ ααိαံ၏ α‘αားα်ားႏွα့္ ေαာα့္α်ား၏ αα္α
α္αႈαို ေα့αာေαာ αာαာαα္ျαα
္αα္။ α‘αံုးα်αα်ၤာ (applied mathematics) αာαာαα္αြα္ trigonometric functions α်ားαို mathematical tools α‘ျαα
္ α‘αံုးျαဳ αါαα္။ Trigonometry ၏αααြဲျαα
္ေαာ spherical trigonometry αိုေαာ့ α‘ာαာαααာႏွα့္ ေαေαΎαာα္း ααာαα္α်ားαြα္ α‘αံုးျαဳαα္။
Angle
In trigonometry an angle is determined by rotating a ray about its endpoint from an initial position to terminal position.
ေαာα့္αα ္αု၏ αူα(α‘α ) αα္αံαို initial side αုေαααΏαီး ေαြααွ်ားαα္αံαို terminal side αု ေαααα္။ ေαာα့္α်ားαို coordinate ျαα္αီαြα္ ေααျαေαာα‘αါ positive x-axis αို initial side αု αα္αွα္αα္။
Positive and Negative Angles
Angles measured from the X-axis in an anticlockwise direction are positive angles.
Angles measured from the X-axis in an clockwise direction are negative angles.
ေαာα့္αα ္αု αိုαα္αွာ α‘αိုα္းα‘αာ (magnitude) ျαα ္ေαာေαΎαာα့္ αααိ αα္αိုးαြα္ α‘ေαါα္းα‘ႏႈα္ αα္αိုး αα္αွα္ α်α္ ααွိαါ။ Positive and negative αု αြဲျαား αα္αွα္ျαα္းαွာ α₯ီးαα္αာ (direction) αို αα္αွα္ျαα္း ျαα ္αါαα္။ initial side αွ terminal side αိုα αာαီαα္αံ ေျαာα္းျαα္ (anticlockwise direction) α‘αိုα္းေαြααွ်ားαွ်α္ positive angle αု αα္αွα္αΏαီး αာαီ αα္αံα‘αိုα္း (clockwise direction) ေαြααွ်ားαွ်α္ negative angle αု αα္αွα္αα္။
Radian Measure of an Angle
The radian measure of an angle is the ratio of the length of the arc (s) whose centre is at the vertex of the angle to the radius (r).
ေαာα့္αα ္αု၏ radian measure αိုαα္αွာ αိုေαာα့္၏ ေαာα့္α ြα္းαွα္αို ααိုျαဳေαာ α α္αိုα္းαα ္αု၏ ေαာα့္αα္αံ ႏွα ္αုαΎαား α‘αα္းαိုα္းα‘α်ား (s) ႏွα့္ α‘α်α္းαα္ (r) αိုα၏ α‘α်ိဳးျαα ္αα္။
Relation between Degree and Radian Measure
Six Trigonometric Ratios of a Right Angle
Trigonometric ratios αိုαα္αွာ ေαာα့္αွα္ααိαံαα ္αု၏ ေαာα့္αွα္ααုα္ေαာ ေαာα့္αα ္αုႏွα့္ α‘αားα်ား ၏ αα္α α္αႈ α‘α်ိဳးα်ား ျαα ္αα္။ ေαာα့္αွα္ααိαံ αα ္αု၏ Trigonometric Ratios α်ားαို ေαာ္ျαααွ်α္-
Identities
Trigonometric Ratios of Special Angles
Trigonometric Ratios of Any Angles
ေαာα့္α‘αိုα္းα‘αာ α‘ားαံုးα‘αြα္ α‘α်ိဳးα်ားαို αွာႏိုα္αα္ unit circle αိုေα့αာαα္။ Unit circle αိုαα္ αွာ Radius ααာα 1 unit αွိေαာ circle αα ္αုျαα ္αα္။ Circle ၏ ααို(centre) αို X-Y plane(Cartesian Plane) ၏ origin α‘ျαα ္αα္αွα္αα္။ Trigonometric ratios αွာαိုေαာ ေαာα့္၏ initial side α‘ျαα ္ positive X-axis αို αα္αွα္αα္။
αα္αါαα္....................။
Trigonometry αိုαာ ααိαံαဲα αα္αိုα္ေαာ αα်ၤာαာαာαα္αိုα ေααုα် α‘αိααΈါα္αြα့္αို ႏိုα္αါαα္။ ααိαံ၏ α‘αားα်ားႏွα့္ ေαာα့္α်ား၏ αα္α
α္αႈαို ေα့αာေαာ αာαာαα္ျαα
္αα္။ α‘αံုးα်αα်ၤာ (applied mathematics) αာαာαα္αြα္ trigonometric functions α်ားαို mathematical tools α‘ျαα
္ α‘αံုးျαဳ αါαα္။ Trigonometry ၏αααြဲျαα
္ေαာ spherical trigonometry αိုေαာ့ α‘ာαာαααာႏွα့္ ေαေαΎαာα္း ααာαα္α်ားαြα္ α‘αံုးျαဳαα္။Angle
In trigonometry an angle is determined by rotating a ray about its endpoint from an initial position to terminal position.ေαာα့္αα ္αု၏ αူα(α‘α ) αα္αံαို initial side αုေαααΏαီး ေαြααွ်ားαα္αံαို terminal side αု ေαααα္။ ေαာα့္α်ားαို coordinate ျαα္αီαြα္ ေααျαေαာα‘αါ positive x-axis αို initial side αု αα္αွα္αα္။
Positive and Negative Angles
Angles measured from the X-axis in an anticlockwise direction are positive angles.Angles measured from the X-axis in an clockwise direction are negative angles.
ေαာα့္αα ္αု αိုαα္αွာ α‘αိုα္းα‘αာ (magnitude) ျαα ္ေαာေαΎαာα့္ αααိ αα္αိုးαြα္ α‘ေαါα္းα‘ႏႈα္ αα္αိုး αα္αွα္ α်α္ ααွိαါ။ Positive and negative αု αြဲျαား αα္αွα္ျαα္းαွာ α₯ီးαα္αာ (direction) αို αα္αွα္ျαα္း ျαα ္αါαα္။ initial side αွ terminal side αိုα αာαီαα္αံ ေျαာα္းျαα္ (anticlockwise direction) α‘αိုα္းေαြααွ်ားαွ်α္ positive angle αု αα္αွα္αΏαီး αာαီ αα္αံα‘αိုα္း (clockwise direction) ေαြααွ်ားαွ်α္ negative angle αု αα္αွα္αα္။
Radian Measure of an Angle
The radian measure of an angle is the ratio of the length of the arc (s) whose centre is at the vertex of the angle to the radius (r).
ေαာα့္αα ္αု၏ radian measure αိုαα္αွာ αိုေαာα့္၏ ေαာα့္α ြα္းαွα္αို ααိုျαဳေαာ α α္αိုα္းαα ္αု၏ ေαာα့္αα္αံ ႏွα ္αုαΎαား α‘αα္းαိုα္းα‘α်ား (s) ႏွα့္ α‘α်α္းαα္ (r) αိုα၏ α‘α်ိဳးျαα ္αα္။
Relation between Degree and Radian Measure
Six Trigonometric Ratios of a Right Angle
Trigonometric ratios αိုαα္αွာ ေαာα့္αွα္ααိαံαα ္αု၏ ေαာα့္αွα္ααုα္ေαာ ေαာα့္αα ္αုႏွα့္ α‘αားα်ား ၏ αα္α α္αႈ α‘α်ိဳးα်ား ျαα ္αα္။ ေαာα့္αွα္ααိαံ αα ္αု၏ Trigonometric Ratios α်ားαို ေαာ္ျαααွ်α္-
Identities
Trigonometric Ratios of Special Angles
Trigonometric Ratios of Any Anglesေαာα့္α‘αိုα္းα‘αာ α‘ားαံုးα‘αြα္ α‘α်ိဳးα်ားαို αွာႏိုα္αα္ unit circle αိုေα့αာαα္။ Unit circle αိုαα္ αွာ Radius ααာα 1 unit αွိေαာ circle αα ္αုျαα ္αα္။ Circle ၏ ααို(centre) αို X-Y plane(Cartesian Plane) ၏ origin α‘ျαα ္αα္αွα္αα္။ Trigonometric ratios αွာαိုေαာ ေαာα့္၏ initial side α‘ျαα ္ positive X-axis αို αα္αွα္αα္။
αα္αါαα္....................။
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