Trigonometric Inverse
Inverse of Sin function
Trigonometric Inverse
Inverse trigonometric functions are the inverse functions of the trigonometric functions ( with suitably restricted domains ). Specifically , they are the inverses of the sine , cosine , tangent , cotangent , secant , and cosecant functions . They are used to obtain an angle from any of the angle ' s trigonometric ratios . Inverse trigonometric functions are widely used in engineering , navigation , physics , and geometry .
If we are given that the value of the sine function is 1 / 7 , then the we have to find the radian angle x . sin x = 1 / 7 , so x = sin -1 1 / 7
For inverse to exist , function must be 1:1 , onto
Trigonometric functions are neither 1:1 , nor onto over their natural domains and ranges . Eg y = sin x is not one-one & onto over its natural range & domain .
To make these trigonometric functions one-one & onto , we restrict domains & ranges of these trigonometric functions to ensure existence of their inverses .
Natural domain & range of trigonometric functions
o sine function , i . e ., sine : R→ [– 1 , 1 ] o cosine function , i . e ., cos : R → [– 1 , 1 ] o tangent function , i . e ., tan : R – { x : x = ( 2n + 1 ) π / 2 , n ∈ Z } → R o cotangent function , i . e ., cot : R – { x : x = nπ , n ∈ Z } → R o secant function , i . e ., sec : R – { x : x = ( 2n + 1 ) π / 2 , n ∈ Z } → R – (– 1 , 1 ) o cosecant function , i . e ., cosec : R – { x : x = nπ , n ∈ Z } → R – (– 1 , 1 )
Inverse of Sin function