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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 } .

Similar Problems and Solutions



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 } .

Similar Problems and Solutions



ISI MStat 2019 PSA Problem 12
Outstanding Statistics Program with Applications

Outstanding Statistics Program with Applications

Subscribe to Cheenta at Youtube


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