How can you maximize a trigonometric expression?

In summary, the "Trigonometric Challenge" is a mathematical puzzle that requires strong understanding of trigonometric functions and the ability to solve equations and recognize patterns. It is open to anyone with a passion for math and has benefits such as improving critical thinking and problem-solving skills. There are also resources available for those who need help with the challenge.
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anemone
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Maximize $\sin x \cos y+\sin y \cos z+\sin z \cos x$ for all real $x,\,y$ and $z$.
 
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  • #2
anemone said:
Maximize $\sin x \cos y+\sin y \cos z+\sin z \cos x$ for all real $x,\,y$ and $z$.

from cyclic symmetry it is maximum when $x = y =z$
we get expression = $\frac{3}{2} \sin 2x$ and when $x = y = z= \frac{\pi}{4}$(this is one of the values) it is maximum = $\frac{3}{2}$
 

FAQ: How can you maximize a trigonometric expression?

What is the "Trigonometric Challenge"?

The "Trigonometric Challenge" is a mathematical puzzle that involves solving various trigonometric equations and identifying patterns in the solutions.

What skills are required to complete the "Trigonometric Challenge"?

To successfully complete the "Trigonometric Challenge", one must have a strong understanding of trigonometric functions, such as sine, cosine, and tangent, as well as the ability to solve equations and recognize patterns.

Who can participate in the "Trigonometric Challenge"?

The "Trigonometric Challenge" is open to anyone with a passion for math and a desire to solve challenging problems. It is often used as a competition or activity in schools, but individuals of all ages and backgrounds can participate.

What are the benefits of completing the "Trigonometric Challenge"?

Completing the "Trigonometric Challenge" can improve one's critical thinking skills, problem-solving abilities, and understanding of trigonometric concepts. It can also be a fun and rewarding challenge for those who enjoy math.

Are there any resources available for those who need help with the "Trigonometric Challenge"?

Yes, there are many online resources and textbooks available that provide explanations, examples, and practice problems for trigonometry and the "Trigonometric Challenge". Additionally, seeking help from a math teacher or tutor can also be beneficial.

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