Cryptocurrency Q&A
Why is sin not injective?
Why is sin not injective?
HanbokElegance
Tue Oct 22 2024
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7 answers
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I'm trying to understand why the sine function is not injective. I know that for a function to be injective, every element in the domain must map to a unique element in the codomain, but I'm not sure how this applies to sin specifically.
7 answers
ZenHarmonious
Thu Oct 24 2024
The assertion regarding the function sinx posits that it lacks the property of injectivity on any domain of the real line with a length that is either equal to or greater than π. This fundamental characteristic defines the behavior of sinx within specified intervals.
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CryptoProphet
Wed Oct 23 2024
Therefore, it becomes evident that sinx cannot be considered injective on the entire real line or any substantial portion of it that spans π or longer, due to its inherent periodicity.
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Martina
Wed Oct 23 2024
Injectivity, in mathematical terms, implies that each element in the domain of a function corresponds uniquely to a single element in its range. However, in the case of sinx, this uniqueness breaks down for domains exceeding or equal to π in length.
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Daniele
Wed Oct 23 2024
Additionally, it is worth noting that this characteristic is not unique to sinx but is shared by other periodic functions as well, which similarly fail to meet the criteria for injectivity over extended domains.
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Alessandra
Wed Oct 23 2024
The reason behind this non-injectivity lies in the periodic nature of the sine function. Sinx repeats its values in regular intervals, known as periods, with each period spanning a length of 2π.
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