Finding the Minimum Value of a Mathematical Expression Using Geometry & GeoGebra Visualization

In this video, we solve an intriguing mathematical problem involving trigonometric expressions and their minimum values. We use a geometric interpretation to reframe the problem as finding the shortest distance from a point to a circular region. To verify our theoretical solution, we employ *GeoGebra* to generate random points and visualize their distribution within the given constraints.
🔹 *Key Concepts Covered:*
✔ Transformation of the given expression into geometric form
✔ Minimum distance from a point to a region bounded by circles
✔ Solving using algebraic and graphical methods
✔ GeoGebra simulation to confirm our findings
Watch till the end for a step-by-step breakdown of the solution and an interactive visualization of how the points behave within the given constraints! 🚀
🔔 Don't forget to *like, comment, and subscribe* for more problem-solving insights!

[@gregevgeni1864]

Nice explanation!
Thanks

[@randal_mbappewoei]

this can also be solved by using lagrangian multiplier and find the minimum value of (x-8)²+(y-15)² subject to the constraint x²+y²=49 or 7, and we find that x²+y² =49 gives a min value of 100