CLASS 10 CHAPTER 8 INTRODUCTION TO TRIGONOMETRY

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Trigonometric ratios
   The certain ratios involving the sides of a right angled triangle are called Trigonometric ratios. 
       Suppose: b is the base
       h is the hypotenuse
       p is perpendicular then,

       


      sin A=Perpendicular    =    P
                  Hypotenuse              H
       cos A=      Base            =    B
                   Hypotenuse            H
       tan A=  Perpendicular  =    P
                       Base                      B
       Reciprocals of the ratios are:
       Cosec A= 1/sin A= h/p
       Sec A= 1/cos A= h/b
       Cot A= 1/tan A= b/p
         •   Sin □ is a single symbol and sin cannot be detached from ‘□’. And sin □ ≠ sin X □.
       This remark is true for other ratios as well
  Trigonometric /Ratios of some specific angles
       The specific angles are 0°, 30°,45°, 60°, 90°. These are given in the following table
       
       The value of sin A increases from 0 to 1, as A increases from 0° to 90°
       The value of cosA decreases from 1 to 0, as A increases from 0° to 90°
       The value of tan A increases from 0 to infinity, as A from increases 0° to 90°
       √2 = 1.414 and √3 = 1.732
     Trignometric identities
         •   Cos2 A+ sin2 A = 1
         •   1+tan2 A= sec2 A
         •   Cot2 A+1= cosec2 A
     Trigonometric ratios of complementary angles
       Two angles are said to be complementary if their sum equals to 90°
            1. Sin (90°-A)= cos A
            2. Cos (90°-A)= sin A
            3. Tan (90°-A)= cotA
            4. Cot (90°-A)= tan A                                                      5. Sec (90°- A)= cosec A
            6. Cosec( 90°- A)= sec A
     Note
             Tan 0°= cot 90°= 0
             Sec0°=cosec 90°=1
             Sec 90°, cosec 0°, cot 0° and tan 90  are not defined

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