From b1f21be80b5b76df1467c8b570ba5fd925c56b16 Mon Sep 17 00:00:00 2001 From: Fang Liu Date: Wed, 19 Apr 2023 17:00:36 +0800 Subject: [PATCH] Update trig_functions.qmd some typos. --- quarto/precalc/trig_functions.qmd | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/quarto/precalc/trig_functions.qmd b/quarto/precalc/trig_functions.qmd index 05d9b6b..89f113f 100644 --- a/quarto/precalc/trig_functions.qmd +++ b/quarto/precalc/trig_functions.qmd @@ -206,7 +206,7 @@ Which for sake of memory we will say is $1/6$ (a $5$ percent error). So that ans 30 * 3 / 6 ``` -Similarly, you can use your thumb instead of your first. To use your first you can multiply by $1/6$ the adjacent side, to use your thumb about $1/30$ as this approximates the tangent of $2$ degrees: +Similarly, you can use your thumb instead of your fist. To use your fist you can multiply by $1/6$ the adjacent side, to use your thumb about $1/30$ as this approximates the tangent of $2$ degrees: ```{julia} @@ -550,7 +550,7 @@ The approximation error is about $2.7$ percent. ##### Example -The AMS has an interesting column on [rainbows](http://www.ams.org/publicoutreach/feature-column/fcarc-rainbows) the start of which uses some formulas from the previous example. Click through to see a ray of light passing through a spherical drop of water, as analyzed by Descartes. The deflection of the ray occurs when the incident light hits the drop of water, then there is an *internal* deflection of the light, and finally when the light leaves, there is another deflection. The total deflection (in radians) is $D = (i-r) + (\pi - 2r) + (i-r) = \pi - 2i - 4r$. However, the incident angle $i$ and the refracted angle $r$ are related by Snell's law: $\sin(i) = n \sin(r)$. The value $n$ is the index of refraction and is $4/3$ for water. (It was $3/2$ for glass in the previous example.) This gives +The AMS has an interesting column on [rainbows](http://www.ams.org/publicoutreach/feature-column/fcarc-rainbows) the start of which uses some formulas from the previous example. Click through to see a ray of light passing through a spherical drop of water, as analyzed by Descartes. The deflection of the ray occurs when the incident light hits the drop of water, then there is an *internal* deflection of the light, and finally when the light leaves, there is another deflection. The total deflection (in radians) is $D = (i-r) + (\pi - 2r) + (i-r) = \pi + 2i - 4r$. However, the incident angle $i$ and the refracted angle $r$ are related by Snell's law: $\sin(i) = n \sin(r)$. The value $n$ is the index of refraction and is $4/3$ for water. (It was $3/2$ for glass in the previous example.) This gives $$ @@ -587,7 +587,7 @@ $$ \cos((n+1)\theta) = 2\cos(n\theta) \cos(\theta) - \cos((n-1)\theta). $$ -Let $T_n(x) = \cos(n \arccos(x))$. Calling $\theta = \arccos(x)$ for $-1 \leq x \leq x$ we get a relation between these functions: +Let $T_n(x) = \cos(n \arccos(x))$. Calling $\theta = \arccos(x)$ for $-1 \leq x \leq 1$ we get a relation between these functions: $$