Introduction to Trigonometry-Notes

•   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,

       

       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

                    Note

       Tan 0°= cot 90°= 0

       Sec0°=cosec 90°=1

       Sec 90°, cosec 0°, cot 0° and tan 90° are not defined