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Trigonometry & natural numbers | PRMO 2017 | Question 11

Try this beautiful problem from the Pre-RMO, 2017 based on Trigonometry & natural numbers.

Trigonometry & natural numbers - PRMO 2017


Let f(x) =sin\frac{x}{3}+cos\frac{3x}{10} for all real x, find the least natural number x such that f(n\pi+x)=f(x) for all real x.

  • is 107
  • is 60
  • is 840
  • cannot be determined from the given information

Key Concepts


Trigonometry

Least natural number

Functions

Check the Answer


Answer: is 60.

PRMO, 2017, Question 11

Plane Trigonometry by Loney

Try with Hints


here f(x) =sin\frac{x}{3}+cos\frac{3x}{10}

period ofsin\frac{x}{3} is 6\pi

period of cos\frac{3x}{10} is \frac{20\pi}{3}

Lcm=\frac{60\pi}{3} \Rightarrow n=60.

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Try this beautiful problem from the Pre-RMO, 2017 based on Trigonometry & natural numbers.

Trigonometry & natural numbers - PRMO 2017


Let f(x) =sin\frac{x}{3}+cos\frac{3x}{10} for all real x, find the least natural number x such that f(n\pi+x)=f(x) for all real x.

  • is 107
  • is 60
  • is 840
  • cannot be determined from the given information

Key Concepts


Trigonometry

Least natural number

Functions

Check the Answer


Answer: is 60.

PRMO, 2017, Question 11

Plane Trigonometry by Loney

Try with Hints


here f(x) =sin\frac{x}{3}+cos\frac{3x}{10}

period ofsin\frac{x}{3} is 6\pi

period of cos\frac{3x}{10} is \frac{20\pi}{3}

Lcm=\frac{60\pi}{3} \Rightarrow n=60.

Subscribe to Cheenta at Youtube


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