How do you find the exact value of #arcsin(sin(2))#?

Answer 1

The exact value of #arcsin(sin(2))# is simply #2#.

Whenever we take the arcsin of sin, or the arccos of cos, or the inverse of any trig function, they always cancel each other out. So #arctan(tan(3))=3#, #arcsin(sin(1))=1#, and so on.

The reason for this is because to find the arcsin of a given number, for instance, #arcsinx#, we are basically asking "When will the sin of some number equal #x#?"

So with this problem, instead of #x# we have the arcsin of sin. Thus we are basically asking "When will the sin of some number equal #sin(2)#?"

#sin(n)=sin(2)#

So #n# is clearly #2#.

This also works no matter order we're taking #sin# and #arcsin# in. So for example,

#sin(arcsin(0))=0#

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Answer 2

Anna Andrews

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.