Question #92a8b

1 Answer
A. S. Adikesavan
May 7, 2016

You read it as arc sin ( sin (#5^o#)) This is the angle whose sine is sin #5^o#.So, the answer is #5^o#. If the angle is 5 radian = 286.5#^o#, nearly, the answer is 5 radian. See explanation.. . .

Explanation:

I have now added some more clarifications at the end, to make all unambiguous.
If an inverse operator and the operator, or vice versa, are applied in succession on an operand a, the result is a.

Examples:

#10^log a=a#.

#arc tan tan a=a#

Here, arc sin sin 5 = 5.

This return of 5 is independent of the unit used for measurement.

Also, if it is 5 radian = #286.5^o#, in the fourth quadrant, sin 5 is negative. It is important, that if this angle is one from many in the general value, the answer is 5 only and swapping to another is not permitted.

By definition, the rule is both #O^(-1)O and OO^(-1)# are equivalent to multiplication by the unit operator 1.

#O^(-1)O a = a and OO^(-1) b = b#
The value entered as the operand is returned... . .
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