From 1b117ebd8ff269c32f5d65e920479c7b09f10364 Mon Sep 17 00:00:00 2001
From: Daniel Chen <eggyrules@gmail.com>
Date: Tue, 26 Nov 2019 14:38:58 +0000
Subject: [PATCH] Fix trig grammar

---
 Grade 10/Math/MPM2DZ/Unit 4: Trigonometry.md | 26 ++++++++++----------
 1 file changed, 13 insertions(+), 13 deletions(-)

diff --git a/Grade 10/Math/MPM2DZ/Unit 4: Trigonometry.md b/Grade 10/Math/MPM2DZ/Unit 4: Trigonometry.md
index 2b32f81..d76a5dc 100644
--- a/Grade 10/Math/MPM2DZ/Unit 4: Trigonometry.md	
+++ b/Grade 10/Math/MPM2DZ/Unit 4: Trigonometry.md	
@@ -9,7 +9,7 @@
 
   - <img src="https://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/58a52a99-05da-4595-88b8-2cbca91e8bbf.gif" width="300">   
 
-2. ```Supplementary Angle Triangle``` (SAT)     
+2. ```Supplementary Angle Theorem``` (SAT)     
   - When two angles add up to 180 degrees     
 
   - <img src="https://embedwistia-a.akamaihd.net/deliveries/cdd1e2ebe803fc21144cfd933984eafe2c0fb935.jpg?image_crop_resized=960x600" width="500">   
@@ -69,7 +69,7 @@ If two angles and the **contained** side of a triangle are respectively equal to
 
 <img src="https://www.onlinemath4all.com/images/trianglecongruenceandsimilarity4.png" width="500">
 
-## Similary Triangles
+## Similar Triangles
 `Similar`: Same shape but different sizes (one is an enlargement of the other)
 
 ### Properties
@@ -93,7 +93,7 @@ Three pairs of corresponding sides are in the **same ratio**
 
 <img src="https://docs.google.com/drawings/d/snd5DSjJuOz9Lql5RgzUxCw/image?parent=1ltNI2q_ajTaJyAGt7C7GLY0uwh9LbBOfjW1B4Og_KwM&rev=59&h=188&w=398&ac=1" width="500">
 
-### Side Angle Side similarity (RAR $`\sim`$)
+### Side-Angle-Side similarity (RAR $`\sim`$)
 Two pairs of corresponding sides are proportional and the **contained** angle are equal.
 
 <img src="http://804369586450478528.weebly.com/uploads/4/5/2/6/45266747/775263614.png?367" width="400">
@@ -105,7 +105,7 @@ Two pairs of corresponding angles are equal. In the diagram below, we can solve
 
 
 
-## Primary Trigonometry Ratios
+## Primary Trigonometric Ratios
 
 |Part Of Triangle|Property|
 |:---------------|:-------|
@@ -113,7 +113,7 @@ Two pairs of corresponding angles are equal. In the diagram below, we can solve
 |Opposite|The side opposite to the reference angle|
 |Adjacent|The side next to the reference agnle|
 
-**Remember**: Primary Trigonometry ratios are only used to find the **acute** angles or sides of a **right-angled** triangle
+**Remember**: Primary trigonometric ratios are only used to find the **acute** angles or sides of a **right-angled** triangle
 
 ### SOH CAH TOA
 
@@ -151,9 +151,9 @@ Also, for some trigonometry identities:
 **If you are finding the sides or agnles of an `oblique triangle` given 1 side, its opposite angle and one other side or angle, use the sine law.**
 
 ### Ambiguous Case
-The ambiguous case arises in the SSA or (ASS) case of an triangle, when you are given angle side side. The sine law calculation may need to 0, 1, or 2 solutions.
+The ambiguous case arises in the SSA or (ASS) case of an triangle, when you are given angle-side-side. The sine law calculation may need to give 0, 1, or 2 solutions.
 
-In the ambigouous case, if $`\angle A, a, b`$ are given, the height of the triangle is $`h= b\sin A`$
+In the ambiguous case, if $`\angle A, a, b`$ are given, the height of the triangle is $`h= b\sin A`$
 
 
 |Case|If $`\angle A`$ is **acute**|Condition|# & Type of triangles possible|
@@ -165,7 +165,7 @@ In the ambigouous case, if $`\angle A, a, b`$ are given, the height of the trian
 
 |Case|If $`\angle A`$ is **obtuse**|Condition|# & Type of triangles possible|
 |:---|:----------------------------|:--------|:-----------------------------|
-|5   |<img src="http://jwilson.coe.uga.edu/EMT668/EMAT6680.2001/Mealor/EMAT%206700/law%20of%20sines/Law%20of%20Sines%20ambiguous%20case/image5.gif" width="200">|$`a \le b`$|no triangle exists|
+|5   |<img src="http://jwilson.coe.uga.edu/EMT668/EMAT6680.2001/Mealor/EMAT%206700/law%20of%20sines/Law%20of%20Sines%20ambiguous%20case/image5.gif" width="200">|$`a \le b`$|no triangles exist|
 |6   |<img src="https://www.mathopenref.com/images/constructions/constaltitudeobtuse/step0.gif" width="300">|$`a \gt b`$|one triangle exists|
 
 
@@ -177,15 +177,15 @@ In any $`\triangle ABC`$, $`c^2 = a^2 + b^2 - 2ab\cose C`$
 
 ## Directions
 
-`Bearins`: **Always** start from **North**, and goes **clockwise**
-`Direction`: Start from the first letter (N, E, S, W), and go that many degrees to the second letter (N, E, S, W)
+`Bearings`: **Always** start from **North**, and goes **clockwise**
+`Direction`: Start from the first letter (N, E, S, W), and go that many degrees directly to the second letter (N, E, S, W)
 
-**Note:** Northeast, Southeast, NorthWest etc. all have 45 degrees to the left or the right from their starting degree (0, 90, 180, 270)
+**Note:** Northeast, southeast, northwest etc. all have 45 degrees to the left or the right from their starting degree (0, 90, 180, 270)
 
 ## 2D Problems
-**Note:** Watch out for the case where you don't know which side the 2 things (buildings, boats etc) are, they can result in 2 answers
+**Note:** Watch out for the case where you don't know which side the 2 things (buildings, boats, etc.) are, they can result in 2 answers
 
 ## 3D problems
-**Note:** Use angle theorems to find bearing/direction angle, and to help with the problem in general. Apply sine law, cosine law, and primary trigonometry ratios whenever necessary.
+**Note:** Use angle theorems to find bearing/direction angle, and to help with the problem in general. Apply sine law, cosine law, and primary trigonometric ratios whenever necessary.