DM'S Mathematics

DM'S Mathematics This page will demonstrate, the unit circle, graphing sine/ cosine functions, inverse trig functions, right triangle trig, oblique triangles, & identities.

Inverse Trigonometric Functions - Stephanie Perez
(y) Inverse Trig Function
The inverse SINE function is defined by y= arcsin x if and only if sin= x
The domain of y = arcsin x is [ -1, 1]
The range of y = arcsin x [ -𝝅 / 2, 𝝅 / 2]
* Arcsin values only come from Q1 *
(x) Inverse Trig Function
The inverse COSINE function is defined by y = arccos x if and only if cos y= x
(y= arccos x is the an

gle whose cosine is x)
The domain of y= arccos x is [ -1, 1]
The range of y= arccos x is [ 0, 𝝅]
*Cosine can be found in Q1 and Q2
Solving Using a Triangle
It would be very convinient of you to know SOHCAHTOA. That way it would be a lot easier. Not only that drawing a triangle would definitely help out. You will use the same previous steps if you encounter arcsin or arccos but there's also arctan. When arctan appears you should know that that represents (y/x) but there would be more about this is a separate document to get a better understanding of it. HELPFUL HITS
Make sure to use a unit circle! This will make this topic a lot easier! SOH/CAH/TOA
(S)= sine and its set up to look like (O)pposite/ (H)ypotenuse in fraction form
(C)= cosine and it's set up to look like (A)djecent/ (H)ypotenuse in fraction form
(T)= tan and it's set up to look like (O)pposite/ (A)djecent in fraction form

Cos (x) -------------------> Sec (1/x)
Sin (y) --------------------> Csc (1/y)
Tan (y/x) ------------------> Cot (x/y)

Oblique Triangles

Law of Sines
*ONLY for NON RIGHT ANGLE TRIANGLES*
Is it a right triangle? If it is then you will use SOHCAHTOA
If it is not then you will use Law of Sines
Law of Sines: Sin A = Sin B = Sin C
a b c

a = b = c
Sin A Sin B Sin C
The best way to represent this would be by using a Triangle.
* How fat/thin the angle is determines how long the line is*
* You need to know 2 sets*

The Ambiguous Case
This occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA). Height= b x Sin A
How to determine the number of triangles we are going to have
If a=h, then there is only ONE triangle
If a is < h, there is NO triangle
If a > b, there is ONE triangle
If h < a < b, there is TWO triangles
There will be more examples is the “Photos” section

Law of Cosine
It is a different concept then Law of Sines but we of course still use triangle! a²= b² + c² - 2 x c x b x cos A
b²= a² + c² - 2 x a x c x cos B
c²= b² + a² -2 x a x b x cos C
Further explanations and examples are to be posted in the photos and home section. Area of an Oblique Triangle
* Two sides and Angle SSA*
area= ½ bc x Sin A area= ½ ac x Sin B area= ½ ab x Sin C

Make sure to label the triangle ABC and abc based on the side and angles provided on the problem. More examples and into depth explanations on how to do it will be provided in the videos, photos, and home.

SOHCAHTOA
12/04/2017

SOHCAHTOA

Trigonometric Identities https://www.youtube.com/watch?v=ep5vjIY5kqE
12/04/2017

Trigonometric Identities
https://www.youtube.com/watch?v=ep5vjIY5kqE

This video shows you a simplified way in verifying trigonometric identities whenever you have to prove or verify a trig identity. Trigonometry Online Course:...

12/04/2017

Inverse Trigonometric Functions - Stephanie Perez
(y) Inverse Trig Function
The inverse SINE function is defined by y= arcsin x if and only if sin= x
The domain of y = arcsin x is [ -1, 1]
The range of y = arcsin x [ -𝝅 / 2, 𝝅 / 2]
* Arcsin values only come from Q1 *
(x) Inverse Trig Function
The inverse COSINE function is defined by y = arccos x if and only if cos y= x
(y= arccos x is the angle whose cosine is x)
The domain of y= arccos x is [ -1, 1]
The range of y= arccos x is [ 0, 𝝅]
*Cosine can be found in Q1 and Q2
Solving Using a Triangle
It would be very convinient of you to know SOHCAHTOA. That way it would be a lot easier. Not only that drawing a triangle would definitely help out. You will use the same previous steps if you encounter arcsin or arccos but there's also arctan. When arctan appears you should know that that represents (y/x) but there would be more about this is a separate document to get a better understanding of it.

HELPFUL HITS
Make sure to use a unit circle! This will make this topic a lot easier!
SOH/CAH/TOA
(S)= sine and its set up to look like (O)pposite/ (H)ypotenuse in fraction form
(C)= cosine and it's set up to look like (A)djecent/ (H)ypotenuse in fraction form
(T)= tan and it's set up to look like (O)pposite/ (A)djecent in fraction form

Cos (x) -------------------> Sec (1/x)
Sin (y) --------------------> Csc (1/y)
Tan (y/x) ------------------> Cot (x/y)

Oblique Triangles

Law of Sines
*ONLY for NON RIGHT ANGLE TRIANGLES*
Is it a right triangle?
If it is then you will use SOHCAHTOA
If it is not then you will use Law of Sines
Law of Sines: Sin A = Sin B = Sin C
a b c

a = b = c
Sin A Sin B Sin C
The best way to represent this would be by using a Triangle.
* How fat/thin the angle is determines how long the line is*
* You need to know 2 sets*

The Ambiguous Case
This occurs when one uses the law of sines to determine missing measures of a triangle when given two sides and an angle opposite one of those angles (SSA).
Height= b x Sin A
How to determine the number of triangles we are going to have
If a=h, then there is only ONE triangle
If a is < h, there is NO triangle
If a > b, there is ONE triangle
If h < a < b, there is TWO triangles
There will be more examples is the “Photos” section

Law of Cosine
It is a different concept then Law of Sines but we of course still use triangle!
a²= b² + c² - 2 x c x b x cos A
b²= a² + c² - 2 x a x c x cos B
c²= b² + a² -2 x a x b x cos C
Further explanations and examples are to be posted in the photos and home section.
Area of an Oblique Triangle
* Two sides and Angle SSA*
area= ½ bc x Sin A area= ½ ac x Sin B area= ½ ab x Sin C

Make sure to label the triangle ABC and abc based on the side and angles provided on the problem. More examples and into depth explanations on how to do it will be provided in the videos, photos, and home.

Simplifying trig expressions by using the reciprocal identities
12/04/2017

Simplifying trig expressions by using the reciprocal identities

http://www.freemathvideos.com In this video series I will show you how to simplify trigonometric expressions. We will simplify these expression to either a s...

Graphing Sine and Cosine
12/04/2017

Graphing Sine and Cosine

Graphing Sine and Cosine With Different Coefficients, Ex 1. In this video, I talk about how to find the amplitude and period of a couple of functions. In the...

RIGHT TRIANGLE TRIGONOMETRY PRACTICE !!
12/04/2017

RIGHT TRIANGLE TRIGONOMETRY PRACTICE !!

Learn the basics of trigonometry: What are sine, cosine, and tangent? How can we use them to solve for unknown sides and angles in right triangles?

SPECIAL RIGHT TRIANGLES PRACTICE !!
12/04/2017

SPECIAL RIGHT TRIANGLES PRACTICE !!

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

PYTHAGOREAN THEOREM - which is a leading factor to SOHCAHTOA
12/04/2017

PYTHAGOREAN THEOREM - which is a leading factor to SOHCAHTOA

Look at a right triangle With a 90 degree right angle Across from the right angle is the hypotenuse It's no surprise the hypotenuse is the longest side Now h...

SOHCAHTOA SOHCAHTOASOHCAHTOA
12/04/2017

SOHCAHTOA
SOHCAHTOA
SOHCAHTOA

http://jonathanmann.net SOHCAHTOA SOHCAHTOA SOHCAHTOA SOHCAHTOA SOHCAHTOA SOHCAHTOA Sine Opposite Hypotenuse Sine Opposite Hypotenuse Sine Opposite Hypotenus...

SPECIAL RIGHT TRIANGLES - this video is explaining on what the overall ideal image of Special Right Triangles.
12/04/2017

SPECIAL RIGHT TRIANGLES - this video is explaining on what the overall ideal image of Special Right Triangles.

MIT grad shows how to "solve a right triangle" using trig. More videos with Nancy coming in 2017! To skip ahead: 1) For HOW to CHOOSE A TRIG FUNCTION to solv...

Right Triangle Trigonometry Is the concept of the following factors : Pythagorean Theorem : the square of the length of ...
12/04/2017

Right Triangle Trigonometry
Is the concept of the following factors :

Pythagorean Theorem : the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

SOHCAHTOA : A way of remembering how to compute the sine, cosine, and tangent of an angle. SOH stands for Sine equals Opposite over Hypotenuse. CAH stands for Cosine equals Adjacent over Hypotenuse. TOA stands for Tangent equals Opposite over Adjacent.

Special Right Triangles : is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.

Note and some examples
12/04/2017

Note and some examples

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