Trigonometry
      Basic relationships between trigonometric functions of the same angle
          Basic relationships between trigonometric functions of the same angle shown in the unit circle
         Basic relationships between trigonometric functions of the same angle shown in the tabular form
         Basic relationships between trigonometric functions of the same angle, examples
Basic relationships between trigonometric functions of the same angle shown in the unit circle
Given relations between the trigonometric functions of the same angle, expressed by absolute value, are included in the definitions of the functions in right triangles shown in Fig. a - d, and included in the table below.
Basic relationships between trigonometric functions shown in the tabular form
Basic relationships between trigonometric functions of the same angle, examples
Example:   Find values of other trigonometric functions of an angle a, if given sin a = - 4/5 and
270 < a < 360.
Solution:   Since a is a forth-quadrant angle, then
Example:   Find the value of
Solution:   Dividing the numerator and the denominator by cos2 x,
Example:   Prove the identity
Solution:  
Example:   Given sin x + cos x = a,  find  sin4 x + cos4 x .
Solution:   Since   sin2 x + cos2 x = 1  then,
(sin2 x + cos2 x)2 = sin4 x + cos4 + 2sin2 x cos2 x = 1   or   sin4 x + cos4 = 1 - 2sin2 xcos2 x.   
As given  sin x + cos x = a  then,   (sin x + cos x)2 = a2   or   sin2 x + cos2 x + 2sin x cos x = a2
therefore,  sin x cos x = (a2 - 1)/2   and it follows that    sin4 x + cos4 = 1 - (a2 - 1)2/2.
Trigonometry contents A
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