Ce diaporama a bien été signalé.
Nous utilisons votre profil LinkedIn et vos données d’activité pour vous proposer des publicités personnalisées et pertinentes. Vous pouvez changer vos préférences de publicités à tout moment.

PPT on Trigonometric Functions. Class 11

59 745 vues

Publié le

The data is present below the pictures so as to edit it as per your needs. I wanted to use good fonts and this was the only way i could do it as the fonts would not be available on your computer.

Publié dans : Formation
  • Best dissertation help you can get, thank god a friend suggested me ⇒⇒⇒WRITE-MY-PAPER.net ⇐⇐⇐ otherwise I could have never completed my dissertation on time.
       Répondre 
    Voulez-vous vraiment ?  Oui  Non
    Votre message apparaîtra ici
  • Thanks for the help. I also ordered from www.HelpWriting.net
       Répondre 
    Voulez-vous vraiment ?  Oui  Non
    Votre message apparaîtra ici
  • A professional Paper writing services can alleviate your stress in writing a successful paper and take the pressure off you to hand it in on time. Check out, please ⇒ www.WritePaper.info ⇐
       Répondre 
    Voulez-vous vraiment ?  Oui  Non
    Votre message apparaîtra ici
  • Government Auto Auctions US Gov't Surplus & Seized Car Auctions. From $100 or 95% Off. ☺☺☺ https://w.url.cn/s/Ayy1McS
       Répondre 
    Voulez-vous vraiment ?  Oui  Non
    Votre message apparaîtra ici
  • Hi there! I just wanted to share a list of sites that helped me a lot during my studies: .................................................................................................................................... www.EssayWrite.best - Write an essay .................................................................................................................................... www.LitReview.xyz - Summary of books .................................................................................................................................... www.Coursework.best - Online coursework .................................................................................................................................... www.Dissertations.me - proquest dissertations .................................................................................................................................... www.ReMovie.club - Movies reviews .................................................................................................................................... www.WebSlides.vip - Best powerpoint presentations .................................................................................................................................... www.WritePaper.info - Write a research paper .................................................................................................................................... www.EddyHelp.com - Homework help online .................................................................................................................................... www.MyResumeHelp.net - Professional resume writing service .................................................................................................................................. www.HelpWriting.net - Help with writing any papers ......................................................................................................................................... Save so as not to lose
       Répondre 
    Voulez-vous vraiment ?  Oui  Non
    Votre message apparaîtra ici

PPT on Trigonometric Functions. Class 11

  1. 1. 1 TRIGONOMETRY By : Rushikesh Reddy
  2. 2. TRIGONOMETRY  Trigonometry is derived from Greek words trigonon (three angles) and metron ( measure).  Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees.  Triangles on a sphere are also studied, in spherical trigonometry.  Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, on the trigonometric functions, and with calculations based on these functions.
  3. 3. 3
  4. 4.  The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago.  Some experts believe that trigonometry was originally invented to calculate sundials, a traditional exercise in the oldest books.  The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus circa 150 BC, who compiled a trigonometric table using the sine for solving triangles.  Many ancient mathematicians like Aryabhata, Brahmagupta, Ibn Yunus and Al-Kashi made significant contributions in this field(trigonometry). 4 History
  5. 5. Right Triangle  A triangle in which one angle is equal to 90 is called right triangle.  The side opposite to the right angle is known as hypotenuse. AC is the hypotenuse  The other two sides are known as legs. AB and BC are the legs 5 Trigonometry deals with Right Triangles
  6. 6. In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of areas of the squares whose sides are the two legs. In the figure AC2 = AB2 + BC2 6 Pythagoras Theorem
  7. 7.  Sine(sin) opposite side/hypotenuse  Cosine(cos) adjacent side/hypotenuse  Tangent(tan) opposite side/adjacent side  Cosecant(cosec) hypotenuse/opposite side  Secant(sec) hypotenuse/adjacent side  Cotangent(cot) adjacent side/opposite side 7 Trigonometric Ratios
  8. 8. Value of Trigonometric Functions for Angle C 8 Sin  = AB/AC Cos  = BC/AC Tan  = AB/BC Cosec  = AC/AB Sec  = AC/BC Cot  = AC/AB
  9. 9. 0 30 45 60 90 Sine 0 0.5 1/2 3/2 1 Cosine 1 3/2 1/2 1/2 0 Tangent 0 1/ 3 1 3 Not defined Cosecant Not defined 2 2 2/ 3 1 Secant 1 2/ 3 2 2 Not defined Cotangent Not defined 3 1 1/ 3 0 9 Values of Trigonometric Functions
  10. 10. 10 Trigonometric Identities  sin2  + cos2  = 1  1 + tan2  = sec2   1 + cot2  = cosec2   sin(/2) = ±[(1-cos )/2]  Cos(/2)= ±[(1+cos)/2]  Tan(/2)= ±[(1-cos)/(1+cos)]
  11. 11.  There are two Systems of measurements of angles ie., Degree and Radian.  Conversion of degree to radian: Radian= Degree×(л/180)  Conversion of radian to degree: Degree=Radian×(180/л) 11 Conversion of Angles
  12. 12. 12 Angles in Standard Position
  13. 13.  sin (A+B) = sin A cos B + cos A sin B  sin (A-B) = sin A cos B - cos A sin B  cos (A+B) = cos A cos B - sin A sin B  cos(A-B) = cos A cos B + sin A sin B  tan (A+B) = [tan A + tan B] / [1 - tan A tan B]  tan (A-B) = [tan A - tan B] / [1 + tan A tan B] 13 A-B Formula
  14. 14.  sin C - sin D = 2 cos (C+D)/2 sin (C-D)/2  sin C + sin D = 2 sin (C+D)/2 cos (C-D)/2  cos C - cos D = 2 sin (C+D)/2 sin (C-D)/2  cos C + cos D = 2 cos (C+D)/2 cos (C-D)/2 14 C-D Formula
  15. 15.  sin 2θ = 2 sin θ cos θ  cos 2 θ = cos2 θ - sin2 θ  tan 2 θ = 2 tan θ / (1 - tan2 θ)  tan (θ /2) = sin θ / (1 + cos θ)  sin (- θ)=-sin θ  cos(- θ)=cos θ  tan(- θ)=-tan θ 15 2θ Formula
  16. 16.  This field of mathematics can be applied in astronomy, navigation, music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, etc 16 Applications of Trigonometry
  17. 17. Applications of Trigonometry (Astronomy)  Since ancient times trigonometry was used in astronomy.  The technique of triangulation is used to measure the distance to nearby stars.  In 240 B.C., a mathematician named Eratosthenes discovered the radius of the Earth using trigonometry and geometry.  In 2001, a group of European astronomers did an experiment that started in 1997 about the distance of Venus from the Sun. Venus was about 105,000,000 kilometers away from the Sun . 17
  18. 18. 19

×