Introduction to Trigonometry-Notes


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
       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 increases 0° to 90°
       √2 = 1.414 and √3 = 1.732
       Trignometric identitiex
   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
       Tan 0°= cot 90°= 0
       Sec0°=cosec 90°=1
       Sec 90°, cosec 0°, cot 0° and tan 90° are not defined