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can you please explain the important concepts of inverse trignometric functions and also with their formulaes?
Daar Student,
The functions sin-1x, cos-1x, tan-1x, cot-1x, cosec-1x and sec-1x are called inverse circular or inverse trigonometric functions. sin-1x should not be confused with (sin x)-1 which is equal to .Each of the inverse circular functions is multivalued. To make each inverse circular function single valued we define principal values as follows. If x is positive, the principal values of all the inverse circular functions lie between 0 and . If x is negative, the principal values of sin-1x, cosec-1x and tan-1x lie betweenand 0, and those of cos-1x, sec-1x and cot-1x lie between and . From now onwards we take only the principalvalues.Hence sin = x = sin-1x where (range) and x [-1, 1] (domain).This ensures that the function = sin-1x is one-one and onto.Similarly cosec = x = cosec-1x where and x (-, -1] [1, ).cos = x = cos-1x where [0, ] and x [-1, 1].sec = x = sec-1x where and x (-, -1] [1, ).tan = x = tan-1x where and x (-, ).cot = x = cot-1x where (0, ) and x (-, ).The domains and ranges of inverse trigonometric (or inverse circular) functions are:
The graphs of = sin-1x, = cos-1x and = tan-1x are:
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