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juantheron
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Number of real solution of the equation $\sin (\sin (\sin x)) = \cos (\cos (\cos x))$
where $ 0 \leq x\leq 2\pi$
where $ 0 \leq x\leq 2\pi$
Number of Real Solutions for Trigonometric Equation
- Context: MHB
- Thread starter juantheron
- Start date
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SUMMARY
The equation $\sin (\sin (\sin x)) = \cos (\cos (\cos x))$ has exactly 2 real solutions within the interval $0 \leq x \leq 2\pi$. This conclusion is derived from analyzing the behavior of the sine and cosine functions, particularly their nested forms. The periodic nature of these trigonometric functions contributes to the determination of the number of intersections within the specified range.
PREREQUISITES- Understanding of trigonometric functions and their properties
- Familiarity with the concept of periodicity in functions
- Knowledge of solving equations involving nested functions
- Basic skills in graphing functions to visualize intersections
- Study the properties of nested trigonometric functions
- Learn about graphical methods for finding intersections of functions
- Explore the implications of periodicity in trigonometric equations
- Investigate numerical methods for solving transcendental equations
Mathematicians, students studying trigonometry, and anyone interested in solving complex trigonometric equations.
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