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Mathematical Marvels: Insights from the Field

Calculus Castle

Derivative of sinθ using the First Principle

Derivative of \( sinθ \) using the First Principle Let \(y\) = \( sinθ \) ∴ \(y + δy\) = \( sin(θ + δθ) \) ∴ \(δy\) = \( sin(θ + δθ) \) – \( sinθ \)From Trigonometry , we have \( sin(A-B) \) = 2.\( sin \dfrac {(A-B)}{2} \).\( cos \dfrac {(A+B)}{2} \)Using the above…

Derivative of cosθ using the First Principle

Derivative of \( cosθ \) using the First Principle Let \(y\) = \( cosθ \) ∴ \(y + δy\) = \( cos(θ + δθ) \) ∴ \(δy\) = \( cos(θ + δθ) \) – \( cosθ \)From Trigonometry , we have \( cos(A-B) \) = -2.\( sin \dfrac {(A+B)}{2} \).\( sin \dfrac {(A-B)}{2} \)Using the above…

NUMERICAL SOLUTIONS IN PHYSICS

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Atom to Atom: Insights from the Chemical Universe

What is a Chemical Reaction?

A process in which one or more substances get transformed to produce new substance or substances is called a Chemical Reaction. A chemical reaction involves changes in the position of electrons of atoms by restructuring chemical bonds, with no changes to the nuclei of…

Life’s Mysteries Revealed: Exploring Biology

algae biology overview : Algae Biology Overview: A Quick Guide : Algae biology overview: origins, diversity, and uses in ecosystems and industry.

Algae Biology Overview

Explore the diverse world of algae with this algae biology overview—covering forms, pigments, reproduction, and applications.

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