From 3a3932f9bddb6fbea5eb89f1afecb18d0e32064a Mon Sep 17 00:00:00 2001
From: Victor Khaustov <3192677+vi3itor@users.noreply.github.com>
Date: Sat, 21 May 2022 13:21:58 +0900
Subject: [PATCH] Fix sin function

---
 math_differential_calculus.ipynb | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/math_differential_calculus.ipynb b/math_differential_calculus.ipynb
index 9f2983e..244c2a0 100644
--- a/math_differential_calculus.ipynb
+++ b/math_differential_calculus.ipynb
@@ -5908,7 +5908,7 @@
     "\\begin{align*}\n",
     "f'(x) & = \\underset{\\theta \\to 0}\\lim\\dfrac{f(x+\\theta) - f(x)}{\\theta} && \\quad\\text{by definition}\\\\\n",
     "& = \\underset{\\theta \\to 0}\\lim\\dfrac{\\sin(x+\\theta) - \\sin(x)}{\\theta} && \\quad \\text{using }f(x) = \\sin(x)\\\\\n",
-    "& = \\underset{\\theta \\to 0}\\lim\\dfrac{\\cos(x)\\sin(\\theta) + \\sin(x)\\cos(\\theta) - \\sin(x)}{\\theta} && \\quad \\text{since } sin(a+b)=\\cos(a)\\sin(b)+\\sin(a)\\cos(b)\\\\\n",
+    "& = \\underset{\\theta \\to 0}\\lim\\dfrac{\\cos(x)\\sin(\\theta) + \\sin(x)\\cos(\\theta) - \\sin(x)}{\\theta} && \\quad \\text{since } \\sin(a+b)=\\cos(a)\\sin(b)+\\sin(a)\\cos(b)\\\\\n",
     "& = \\underset{\\theta \\to 0}\\lim\\dfrac{\\cos(x)\\sin(\\theta)}{\\theta} + \\underset{\\theta \\to 0}\\lim\\dfrac{\\sin(x)\\cos(\\theta) - \\sin(x)}{\\theta} && \\quad \\text{since the limit of a sum is the sum of the limits}\\\\\n",
     "& = \\cos(x)\\underset{\\theta \\to 0}\\lim\\dfrac{\\sin(\\theta)}{\\theta} + \\sin(x)\\underset{\\theta \\to 0}\\lim\\dfrac{\\cos(\\theta) - 1}{\\theta} && \\quad \\text{bringing out } \\cos(x) \\text{ and } \\sin(x) \\text{ since they don't depend on }\\theta\\\\\n",
     "& = \\cos(x)\\underset{\\theta \\to 0}\\lim\\dfrac{\\sin(\\theta)}{\\theta} && \\quad \\text{since }\\underset{\\theta \\to 0}\\lim\\dfrac{\\cos(\\theta) - 1}{\\theta}=0\\\\\n",