Take the limit of sinx*ln(sinx)

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The discussion centers on finding the limit of sin(x) * ln(sin(x)) as x approaches 0 from the positive side. A participant expresses confusion about the appearance of csc(x) in the limit transformation. Another participant clarifies that sin(x) can be expressed as 1/csc(x), which resolves the confusion. The original poster acknowledges the clarification shortly after posting. The conversation highlights the importance of understanding trigonometric identities in limit problems.
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Homework Statement


Hey
So the question is to take the limit of sinx*ln(sinx)
The first step in the solution shows:
lim
x→0+ ln sinx/csc x

I am confused to where the CSC came from?
Please help
 
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ZooBear said:

Homework Statement


Hey
So the question is to take the limit of sinx*ln(sinx)
The first step in the solution shows:
lim
x→0+ ln sinx/csc x

I am confused to where the CSC came from?
Please help
Hello ZooBear. Welcome to PF !

\displaystyle \sin(x)=\frac{1}{\csc(x)}
 
Thanks a lot! I realized it 5 minutes after I posted.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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