Get inspired by the success stories of our students in IIT JAM MS, ISI  MStat, CMI MSc Data Science.  Learn More 

ISI MStat 2019 PSA Problem 12 | Domain of a function

This is a beautiful problem from ISI MStat 2019 PSA problem 12 based on finding the domain of the function. We provide sequential hints so that you can try.

Domain of a function- ISI MStat Year 2019 PSA Question 12


What is the set of numbers \(x\) in \( (0,2 \pi)\) such that \(\log \log (\sin x+\cos x)\) is well-defined?

  • \( [\frac{\pi}{8},\frac{3 \pi}{8}] \)
  • \( (0,\frac{\pi}{2}) \)
  • \( (0,\frac{ \pi}{4}] \)
  • \( (0,\pi) \cup (\frac{3 \pi}{2}, 2 \pi) \)

Key Concepts


Domain

Basic inequality

Trigonometry

Check the Answer


Answer: is \( (0,\frac{\pi}{2}) \)

ISI MStat 2019 PSA Problem 12

Pre-college Mathematics

Try with Hints


\(logx\) is defined for \( x \in (0,\infty)\).

\(sinx+cosx > 0\).
\(log(sinx+cosx) > 0 \Rightarrow sinx + cosx > 1\)
\( sin(x+\frac{\pi}{4}) > \frac{1}{\sqrt{2}}\)
For \(y\) in \( (0,2 \pi)\) , \(siny > \frac{1}{\sqrt{2}} \iff \frac{\pi}{4} < y < \frac{3\pi}{4 } \)

Hence we have \( 0< x < \frac{\pi}{2 } \) .

ISI MStat 2019 PSA Problem 12
Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube


This is a beautiful problem from ISI MStat 2019 PSA problem 12 based on finding the domain of the function. We provide sequential hints so that you can try.

Domain of a function- ISI MStat Year 2019 PSA Question 12


What is the set of numbers \(x\) in \( (0,2 \pi)\) such that \(\log \log (\sin x+\cos x)\) is well-defined?

  • \( [\frac{\pi}{8},\frac{3 \pi}{8}] \)
  • \( (0,\frac{\pi}{2}) \)
  • \( (0,\frac{ \pi}{4}] \)
  • \( (0,\pi) \cup (\frac{3 \pi}{2}, 2 \pi) \)

Key Concepts


Domain

Basic inequality

Trigonometry

Check the Answer


Answer: is \( (0,\frac{\pi}{2}) \)

ISI MStat 2019 PSA Problem 12

Pre-college Mathematics

Try with Hints


\(logx\) is defined for \( x \in (0,\infty)\).

\(sinx+cosx > 0\).
\(log(sinx+cosx) > 0 \Rightarrow sinx + cosx > 1\)
\( sin(x+\frac{\pi}{4}) > \frac{1}{\sqrt{2}}\)
For \(y\) in \( (0,2 \pi)\) , \(siny > \frac{1}{\sqrt{2}} \iff \frac{\pi}{4} < y < \frac{3\pi}{4 } \)

Hence we have \( 0< x < \frac{\pi}{2 } \) .

ISI MStat 2019 PSA Problem 12
Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com