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Fix trig grammar

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Daniel Chen 2019-11-26 14:38:58 +00:00
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Grade 10/Math/MPM2DZ/Unit 4: Trigonometry.md
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@ -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.