Undergrad Why is the absolute value of sinx used in the integral of cotx?

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SUMMARY

The absolute value of sin(x) is utilized in the integral of cot(x) due to the domain restrictions of the logarithmic function. Specifically, the natural logarithm, ln(sin(x)), is undefined when sin(x) is less than or equal to zero. This necessitates the use of the absolute value to ensure that the argument of the logarithm remains positive, thereby allowing for valid integration of cot(x) across its entire domain.

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  • Understanding of trigonometric functions, specifically sine and cotangent.
  • Knowledge of logarithmic functions and their domains.
  • Familiarity with integral calculus and integration techniques.
  • Basic concepts of absolute values in mathematical expressions.
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  • Study the properties of logarithmic functions, focusing on their domains and restrictions.
  • Explore the integral calculus of trigonometric functions, particularly cotangent and its relationships with sine and cosine.
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  • Investigate the behavior of sin(x) across its periodic intervals to understand when it is positive or negative.
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Why is there a absolute value sign on sinx?
Why is there a absolute value sign on sinx? Does it have to do with the domain of cot x and sin x?
 
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It has to do with the domain of the logarithm. ##\ln \sin x ## isn't defined whenever ##\sin x \leq 0.##
 

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