https://ananasikdev.github.io/blog/categories/math/Recent content in Math on AnanaSeek4JamHugo -- gohugo.ioen-usFri, 15 May 2026 00:00:00 +0000https://ananasikdev.github.io/blog/p/intro_math_1_en/Fri, 15 May 2026 00:00:00 +0000https://ananasikdev.github.io/blog/p/intro_math_1_en/<p>WIP</p> <h2 id="step-1-basics">Step 1: Basics </h2>\[ sin(a + b) = sin(a)cos(b) + sin(b)cos(a) \] \[ cos(a + b) = cos(a)cos(b) - sin(a)sin(b) \] \[ \lim_{x \to a}{(f(x) + g(x))} = \lim_{x \to a}{f(x)} + \lim_{x \to a}{g(x)} \] <p>First remarkable (wonderful) limit:</p> \[ \lim_{\Delta x \to 0}\frac{sin(\Delta x)}{\Delta x} = 1 \] \[ \lim_{\Delta x \to 0}\frac{cos(\Delta x) - 1}{\Delta x} = 0 \] <h2 id="step-2-derivatives-for-sin-and-cos">Step 2: Derivatives for sin and cos </h2>\[ sin'(x) = \lim_{\Delta x \to 0}\frac{sin(x + \Delta x) - sin(x)}{\Delta x} = \lim_{\Delta x \to 0}\frac{sin(x)cos(\Delta x) + sin(\Delta x)cos(x) - sin(x)}{\Delta x} \] \[ \lim_{\Delta x \to 0}\frac{sin(\Delta x)cos(x)}{\Delta x} + \lim_{\Delta x \to 0}\frac{sin(x)cos(\Delta x) - sin(x)}{\Delta x} \] \[ \lim_{\Delta x \to 0}\frac{sin(\Delta x)cos(x)}{\Delta x} + \lim_{\Delta x \to 0}\frac{sin(x)(cos(\Delta x) - 1)}{\Delta x} \] \[ cos(x)\lim_{\Delta x \to 0}\frac{sin(\Delta x)}{\Delta x} + sin(x)\lim_{\Delta x \to 0}\frac{cos(\Delta x) - 1}{\Delta x} \] \[ cos(x) \cdot 1 + sin(x) \cdot 0 \] \[ cos(x) \] <hr> \[ cos'(x) = \lim_{\Delta x \to 0}\frac{cos(x + \Delta x) - cos(x)}{\Delta x} \]