Question is explain why arcsin(sin5) cannot equal to 5
Can someone help me? I plug in that into a calculator but it gives me 5
#explain why arcsin(sin5) cannot equal to 5
ripe pier
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Question is explain why arcsin(sin5) cannot equal to 5
Can someone help me? I p...
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frigid yew
Hmm, that's weird
The arcsine function is usually defined with range [-pi/2, pi]
calm plank
,calc sin(5)
south mountainBOT
Result:
-0.95892427466314
arcsine is defined on [-1,1] and since this number does lie between -1 and 1 we can say that arcsin(sin5)=5
calm plank
Hmm, that's weird
The arcsine function is usually defined with range [-pi/2, pi]
Yes, but here the domain matters, not the range.
lilac monolith
arcsine is defined on [-1,1] and since this number does lie between -1 and 1 we ...
That's not correct.
lilac monolith
arcsin(sin(5)) = arcsin(sin(5 - 2π)) = 5 - 2π
ripe pier
So arcsin(sin5) equals 5?
frigid yew
From Wikipedia,
"Since none of the six trigonometric functions are one-to-one, they must be restricted in order to have inverse functions. Therefore, the result ranges of the inverse functions are proper (i.e. strict) subsets of the domains of the original functions."
lilac monolith
arcsin(sin(x)) is a 2π-periodic function:
arcsin(sin(x)) = π/2 - |x - π/2 - 2πn|, x ∈ [-π/2 + 2πn, 3π/2 + 2πn]
lilac monolith
So arcsin(sin5) equals 5?
No, arcsin(sin(5)) = 5 - 2π.
ripe pier
Why is that?
lilac monolith
Why is that?
Read the definition in my comment above.