logging in or signing up Trigonometric Functions of Acute Angles abheyg2 Download Post to : URL : Related Presentations : Let's Connect Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Copy embed code: Embed: Flash iPad Dynamic Copy Does not support media & animations Automatically changes to Flash or non-Flash embed WordPress Embed Customize Embed URL: Copy Thumbnail: Copy The presentation is successfully added In Your Favorites. Views: 131 Category: Entertainment License: All Rights Reserved Like it (0) Dislike it (0) Added: February 19, 2013 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript TRIGONOMETRIC FUNCTIONS OF ACUTE ANGLES: TRIGONOMETRIC FUNCTIONS OF ACUTE ANGLES By M. Jaya krishna Reddy Mentor in mathematics, APIIIT- Basar , Adilabad ( dt ),A.P. India. Acute Angle: : Acute Angle : ACUTE ANGLE An angle whose measure is greater than zero but less than 90 is called an “acute angle” o Initial ray T E R M I N A L R A YPowerPoint Presentation: S ome O ld H ouses C an’t A lways H ide T heir O ld A ge Commonly used mnemonic for these ratios : Ѳ c a b B C APowerPoint Presentation: Trigonometric functions(also called circular functions) are functions of an angle. History : They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Sumerian astronomers introduced angle measure, using a division of circles into 360 degrees. The sine function was first defined in the “ surya siddhanta ” and its properties were further documented by the fifth century Indian mathematician and astronomer “ Aryabhatta ”. By 10 th century the six trigonometric functions were used.PowerPoint Presentation: Applications : In 240 B.C. a mathematician named “Eratosthenes” discovered the radius of the earth as 4212.48 miles using trigonometric functions.. In 2001 a group of European astronomers did an experiment by using trigonometric functions and they got all the measurement, they calculate the Venus was about 105,000,000 km away from the sun and the earth was about 150, 000, 000 km away. Optics and statics are 2 early fields of Physics that use trigonometry. It is also the foundation of the practical art of surveyingPowerPoint Presentation: 1. Prove that 2. Prove that Sol: Sol:Fundamental Relations:: Fundamental Relations : Squaring and adding both the equations Ѳ c a b C A B From the above diagram, By Pythagorean Rule,PowerPoint Presentation: Squaring and subtracting the equations, we get Similarly, Ѳ c a b C A B From the above diagram, By Pythagorean Rule,PowerPoint Presentation: Example: Prove that sol:PowerPoint Presentation: Ex: Prove that sec 2 Ѳ - cosec 2 Ѳ = tan 2 Ѳ - cot 2 Ѳ Sol: We know that sec 2 Ѳ - tan 2 Ѳ = 1 = cosec 2 Ѳ - cot 2 Ѳ sec 2 Ѳ - tan 2 Ѳ = cosec 2 Ѳ - cot 2 Ѳ sec 2 Ѳ - cosec 2 Ѳ = tan 2 Ѳ - cot 2 Ѳ Example: Prove that Sol: Given thatPowerPoint Presentation: 0 0 30 0 45 0 60 0 90 0 Sin 0 1 Cos 1 0 Tan 0 1 ∞ Cosec ∞ 2 1 Sec 1 2 ∞ Cot ∞ 1 0 Values of the trigonometrical ratios :PowerPoint Presentation: Example: find the value of tan45 0 .sec30 0 - cot90 0 .cosec45 0 Sol: Given that tan45 0 .sec30 0 -- cot90 0 .cosec45 0 = 1 . -- 0. = Example: If cos Ѳ = 3/5, find the value of the other ratios Ѳ 5 4 3 Sol: Given that cos Ѳ = 3/5 = adj / hyp thus using reference triangle adj = 3, hyp = 5,by Pythagorean principle opp = 4THANK YOU: THANK YOU You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.