Arjit-Trigonometry

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Arjit-Trigonometry

  1. 1. Trigonometry<br />™<br />Arjit Saraswat<br />Submitted by :-<br />®<br />Hipparcus – 190 BC to 120 BC – born in Nicaea (now Turkey) was a Greek astronomer who is considered to be one of the first to use trigonometry.<br />
  2. 2. Aryabhatta<br />Indian Mathematician<br />Parts of a Right Triangle<br />B<br />Hypotenuse <br />Perpendicular<br />A<br />C<br />Base<br />Now, imagine that you move from angle A to angle B still facing into the triangle. <br />Imagine that you, the happy face, are standing at angle A facing into the triangle. <br />You would be facing the perpendicular side<br />You would be facing the perpendicular side<br />and standing next to the base.<br />and standing next to the base.<br />The hypotenuse is neither opposite nor adjacent.<br />
  3. 3. Review<br />Pythagorus<br />Samian Mathematician<br />B<br />For Angle A<br />Hypotenuse<br />This is the Perpendicular<br />Perpendicular<br />Perpendicular<br />This is the Base<br />A<br />Base<br />Base<br />B<br />For Angle B<br />This is the Perpendicular<br />Hypotenuse<br />This is the Base<br />A<br />
  4. 4. Trig Ratios<br />Ramanujam<br />Indian Mathematician<br />B<br />Using Angle A to name the sides<br />Hypotenuse<br />Use Angle B to name the sides<br />Perpendicular<br />We can use the lengths of the sides of a right triangle to form ratios. There are 6 different ratios that we can make.<br />A<br />Base<br />The ratios are still the same as before!!<br />
  5. 5. Trig Ratios<br />Euclid<br />Greek Mathematician<br />Hypotenuse<br /><ul><li>Each of the 6 ratios has a name
  6. 6. The names also refer to an angle</li></ul>Perpendicular<br />A<br />Base<br />Sine of Angle A = <br />Cosecant of Angle A = <br />Cosine of Angle A = <br />Secant of Angle A = <br />Cotangent of Angle A = <br />Tangent of Angle A =<br />
  7. 7. Trig Ratios<br />Freitag<br />German Mathematician<br />B<br />Hypotenuse<br />If the angle changes from A to B<br />Perpendicular<br />The way the ratios are made is the same<br />Base<br />Sine of Angle = <br />Cosecant of Angle = <br /> B<br /> B<br />Cosine of Angle = <br /> B<br />Secant of Angle = <br /> B <br />B<br />Cotangent of Angle = <br />Tangent of Angle =<br /> B<br />
  8. 8. Trig Ratios<br />John Dee<br />English Mathematician<br /><ul><li> Each of these ratios has an abbreviation</li></ul>Hypotenuse<br />Perpendicular<br /><ul><li>Sine, Cosine and Tangent ratios are the most common.</li></ul>A<br />Base<br />Sin A =<br />Cosec A=<br />Sine of Angle A = <br />Cosecant of Angle A = <br />Cos A =<br />Sec A =<br />Secant of Angle A = <br />Cosine of Angle A = <br />Cot A =<br />Cotangent of Angle A = <br />Tan A =<br />Tangent of Angle A =<br />
  9. 9. SPHCBHTPB<br />Quetelet<br />Flemish Mathematician<br />B<br />Hypotenuse<br />Here is a way to remember how to make the 3 basic Trig Ratios<br />Perpendicular<br />A<br />Base<br />1) Identify the Perpendicular side and Base for the appropriate angle<br />Remember “SPHCBHTPB” and it means :-<br />Some People Have Curly Beautiful Hair To Preserve Beauty<br />Use the underlined letters to make the word SPH-CBH-TPB<br />
  10. 10. Lame<br />French Mathematician<br />Example<br />B<br />First we will find the Sine, Cosine and<br />Tangent ratios for Angle A.<br />10<br />6<br />Perpendicular<br />A<br />Next we will find the Sine, Cosine, and<br />Tangent ratios for Angle B<br />8<br />Base<br />Remember SPH-CBH-TPB<br />Cosec B = <br />Sin A = <br /> Sec B = <br />Cos A = <br />Cot B = <br />Tan A = <br />
  11. 11. Alberti<br />Italian Mathematician<br />Trigonometric ratios<br />
  12. 12. Created By :-<br />Trigonometry<br />Arjit Saraswat<br />Class : X B<br />School : GMSSS-35,Chd<br />Trigonometry<br />©2010 Saraswat Bros. Ltd.<br />

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