TRIGNOMETRY PROJECT
- 2. CERTIFICATE THIS IS TO CERTIFY THAT RISHIK CHAUDHARY OF CLASS XII-A HAS SUCESSFULLY COMPLETED THE RESEARCH ON THE PROJECT OF POWER POINT PRESENTATION ON TRIGNOMETRY, UNDER THE GUIDANCE OF MRS MONIKA GUPTA , MATHS TEACHER, DURING YEAR,2021- 2022.
- 3. ACKNOWLEDGEMENT IN THE ACCOMPLISHMENT OF THIS PROJECT SUCCESSFULLY, MANY PEOPLE HAVE BESTOWED UPON ME THEIR BLESSINGS AND THE HEART PLEDGED SUPPORT. PRIMARILY I WOULD THANK GOD FOR BEING ABLE TO COMPLETE THIS PROJECT WITH SUCCESS. THEN I WOULD LIKE TO THANK MY PRINCIPLE MRs AASHA SARANSRIVATAVA, MATHS TEACHER MRs MONIKA GUPTA WHOSE VALUABLE GUIDANCE HAS BEEN THE ONCE THAT HELPED ME PATCH THIS PROJECT AND MAKE IT FULL PROOF SUCCESS. THEIR SUGGESTIONS AND THEIR INSTRUCTION HAVE SERVED AS THE MAJOR CONTRIBUTOR TOWARDS THE COMPLETION OF THE PROJECT. THEN I WOULD LIKE TO THANK MY PARENTS AND FRIENDS WHO HAVE HELPED ME WITH THEIR VALUABLE SUGGESTION AND GUIDANCE, WHICH HAS BEEN HELPFUL IN VARIOUS PHASES OF THE COMPLETION OF PROJECT.
- 4. WHAT IS TRIGNOMETRY ? TRIGONOMETRY IS A BRANCH OF MATHEMATICS THAT STUDIES RELATIONSHIPS BETWEEN SIDE LENGTHS AND ANGLES OF TRIANGLES. THE FIELD EMERGED IN THE HELLENISTIC WORLD DURING THE 3RD CENTURY BC FROM APPLICATIONS OF GEOMETRY TO ASTRONOMICAL STUDIES.
- 5. HISTORY OF TRIGNOMETRY THE STUDY OF TRIGNOMETRY WAS FIRST STARTED INIDIA. THE ANCIENT INDIAN MATHAMATICIANS,ARYABHATTA(476 A.D.) BHRAMAGUPTA(598 A.D.),BHASKARA I(600 A.D.) AND BHASKARA II(1114 A.D.) GOT IMPORTANT RESULTS OF TRIGNOMETRY. ALL THIS KNOWLEDGE WENT FROM INDIA TO ARABIA AND THEN FROM THERE TO EUROPE. THE GREEKS HAD ALSO STARTED THE STUDY OF TRIGNOMETRY BUT THEIR APPROACH WAS SO CLUMSY THAT WHEN THE INDIAN APPROACH BECAME KNOWN, IT WAS IMMEDIATELY ADOPTED THROUGHOUT THE WORLD.
- 6. USES OF TRIGNOMETRY TRIGNOMETRY IN ASTRONOMY- ASTRONOMERS USE TRIGONOMETRY TO CALCULATE HOW FAR STARS AND PLANETS ARE FROM EARTH. EVEN THOUGH WE KNOW THE DISTANCES BETWEEN PLANETS AND STARS, THIS MATHEMATICAL TECHNIQUE IS ALSO USED BY NASA SCIENTISTS TODAY WHEN THEY DESIGN AND LAUNCH SPACE SHUTTLES AND ROCKETS.
- 8. TRIGONOMETRY IN CRIMINOLOGY- IN CRIMINOLOGY, TRIGONOMETRY CAN HELP TO CALCULATE A PROJECTILE'S TRAJECTORY, TO ESTIMATE WHAT MIGHT HAVE CAUSED A COLLISION IN A CAR ACCIDENT OR HOW DID AN OBJECT FALL DOWN FROM SOMEWHERE, OR IN WHICH ANGLE WAS A BULLET SHOT, ETC.
- 10. IN ARCHITECTURE- ARCHITECTS USE TRIGONOMETRY TO CALCULATE ROOF SLOPES, LIGHT ANGLES, GROUND SURFACES, STRUCTURAL LOADS AND HEIGHTS OF STRUCTURES, ACCORDING TO EDURITE. ... A SIMPLE EXAMPLE OF TRIGONOMETRY USED IN ARCHITECTURE IS TO FIND THE HEIGHT OF A BUILDING STANDING A CERTAIN DISTANCE FROM THE BUILDING.
- 11. EXAMPLES ARE-
- 12. TRIGNOMETRY IN CARTOGRAPHY- FOR TOPOGRAPHICAL MAPPING, CARTOGRAPHERS USE THE LAWS OF PLANE TRIGONOMETRY WHICH TELLS US THAT THE LENGTH OF JUST ONE SIDE AND 2 ANGLES OF A TRIANGLE IS ALL WE NEED TO KNOW IN ORDER TO DETERMINE THE LENGTH OF THE REMAINING 2 SIDES AND FINAL ANGLE.
- 13. EXAMPLES ARE-
- 14. OTHER USES OF TRIGONOMETRY- TRIGONOMETRY CAN BE USED TO ROOF A HOUSE, TO MAKE THE ROOF INCLINED ( IN THE CASE OF SINGLE INDIVIDUAL BUNGALOWS) AND THE HEIGHT OF THE ROOF IN BUILDINGS ETC. IT IS USED NAVAL AND AVIATION INDUSTRIES.
- 15. SOME OTHER EXAMPLES ARE - OCEANOGRAPHY IN SPOTRTS
- 16. NOW LETS SEE HOW TO CALCULATE TRIGNOMETRIC FUNCTIONS USING TRIANGLE
- 20. NOW LET US SEE THE TRIGNOMETRIC FUNCTIONS USING CIRCLES GREATER THAN 90O
- 23. NOW LET US SEE GRAPHS OF TRIGNOMETRIC FUNCTIONS TO UNDERSTAND BETTER
- 24. GRAPH FOR SIN THETA GRAPH FOR SIN THETA
- 25. GRAPH FOR COS THETA GRAPH FOR COS THETA
- 27. BIBLOGRAPHY SOURCES- (1) CLASS 10 AND 11TH NCERT BOOKS (2) WWW.google.com (3) WWW.Binge. com
- 28. THANKS FOR WATCHING BY-RISHIK CHAUDHARY CLASS-XII-A ROLL NO.-25