USING MIND MAPPING FOR TRIGONOMETRY (SECTI...- Mind Map

USING MIND MAPPING FOR TRIGONOMETRY (SECTIONS 6 & 7)

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Currently, I'm in the process of getting my Associate of Science and I hope once graduated from Lone Star College I wish to continue my education at the University of Houston to get my Bachelor's degree and once done there if I haven't changed my major or career choice by then I will continue to get higher education by getting a Masters degree and god willing get into a Physician assistant program. I understand that most people only go to school because in today's day and age a high school degree doesn't get you far, and if they're a veteran your service only gets you so far as well but speaking from experience as someone who was lost and confused for a very long time after graduating high school and coming back from the navy, there is a light at the end of the tunnel if you keep following it. I love learning new things every time I enroll in each semester that has passed thus far and my curiosity only grows so what I hope to get out of college is the answers to my curiosity but also more questions so I can continue to grow my knowledge of the world. I also would like to apologize for the amount of work that is present on here, there is no excuse I could give you that would justify my lack of work done on this project.

The History of Mind Mapping

To help us understand the importance of mind mapping we first have to know the definition of mind maps to give us a better understanding of its history. Mind Mapping allows the users to organize ideas and break down information into smaller concepts that helps the user understand the information better by allowing them to analyze each piece of the given information.

The history of mind mapping can be traced back to as early as 3rd century AD, fist seen in the workings of a philosopher by the name of Porphyry of Tyron who used it to help classify living organisms. Historians later discovered that Leonardo Da Vinci used a form of mind mapping to take notes.

There was a pair of scientists by the name of Dr. Collins (Alan Collins) and Ross Quillion who developed a theory on human being learned based while using a form of mind mapping. Dr. Collins is known as the father of mind mapping due to his extensive published researched on mind mapping. Tony Buzan was the one who made mind mapping popular by developing a set of rules for one to use during the process.

Some benefits of using mind maps to help the user break down information into smaller fragments in order for them to analyze the information better and perhaps allow the user to dive further into specific topics or allowing them to connect one piece of information to another. This is also a good way for people to take notes because it allows them to see how their mind is grouping pieces of information and it may also give them a physical copy of the information being processed in their minds and could also allow them to make connections, they wound not have caught because they couldn't visualize it in their minds.

Section 6.4: Graphs of Sine and Cosine

determine the amplitude & period of sinusodial functions

graph function of the form y= A cos (wx) using transformation

graph functions of the form y= A sin (wx) using transformations

graph sinusoidal functions using key points

find an equation for a sinusoidal graph

Section 6.6: Phase Shift and Modeling

graph sinusoidal function of the form y= A cos (wx-phi)+B

graph sinusoidal function of the form y= A sin (wx-phi)+B

Build sinusoidal models from data

Section 7.2: The Inverse of Trig Functions (continued)

Key Terms:

Section 7.4: Trigonometric Identities

Key Terms:

Section 7.6: Double & Half Angle Formulas

Key Terms:

Trigonometry

What is Trigonometry? Trigonometry is the measurement of triangles, using its angles and sides.

Section 6.1: Angles, Arc Length, and Circular Motion

Converting From Degrees to Radian/ Concerting from Radian to Degrees

To convert from Radians to Degree you have to multiply the given radian by 180 degrees over pi. An example of this would be (5pi/6) x (180*/pi) = 150*

To convert from Degrees to Radians you have to multiply the given degree by pi/180*. An example of this would be (190*) x (pi/180*) = 19pi/18

Area of a Sector

How do you find the area of a sector? we learned in geometry that the Area of a sector is usually going to be the proportional to the measurement of the central angle (better known as theta)

Area of a Sector Theorem: the area (A) of the sector of a circle

Area of a sector formula: A= (1/2) r^2(theta)

Angles

When two rays have the same vertex is when an angle is formed. There are two sides to an angle; one side is called the Initial side (the bottom portion of an angle) and the other side is called the Terminal side (the upper portion of an angle.)

There is both positive and negative angles in the unit circle, it's important to remember that Positive angles go in a counterclockwise direction, while Negative angles go in a clockwise direction.

An angle can also be known in trigonometry as Theta.

Arc Length

Arc Length: is the distance between two points along a sections' edge/curve.

Subtopic

Circular Motion

Subtopic

Converting between Degrees, Minutes, Seconds, and Decimal Degrees

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Section 6.2: Trigonometric Functions

Finf the exact value of the trigonometric functions using the unit circle

The first thing we need to know when dealing with the unit circle is we have to first memorize the unit circle itself (remember that the unit circle has both degrees and radians indicated on it. It's divided by quadrants on the X and Y axis), and the second thing we have to remember that every unit circle has a radius of 1. example of this is zero is equal to 360 degrees and that is also equal to 2 pi radians; the same way pi is equal to 180 degrees. (0=360*=2pi) (pi=180*)

Another important thing to remember is the Six Trigonometric Identities/rations: Sin of theta = y/r; Csc of theta = r/y; Cos of theta = x/r; Tan of theta = y/r; Cot of theta = x/y; Sec of theta= r/x.

an example of finding the six trig functions of a radian using the unit circle would be done as followed: Find the six trig functions of 5pi/4. 1.) you first have to have a unit circle nearby or have it memorized to locate 5pi/4 on the unit circle to find its X & Y values. 2.) once you have located its X and Y values (negative square root of 2 over 2(x), negative square root of2 over 2 (Y)). 3.) once you have its x and y values you begin to plug them in the given values to the six trigonometric ratios/ identities (remember 'r' represent the radius of the circle which is always going to be 1). ANSWER: Sin of 5pi/4 = negative square root of 2 over 2; Csc of 5pi/4= negative square root of 2; Cos of 5pi/4= negative square root of 2 over 2; Tan of 5pi/4 = 1; Cot of 5pi/4 =1; Sec 5pi/4= negative square root of 2/

To find the six trig functions of an ordered pair that are NOT on the unit circle you use the Pythagorean theorem (The Pythagorean theorem is a^2+b^2= c^2)

find the exact values of the trig functions of 30 & 60 degrees

find the exact values of trig functions of quadrantal angles

Use a calculator to approximate value of the function

Section 6.3: Properties of Trig Functions

Find the domain and the range of trig functions

to help us understand how to find the domain of a trig functions we should use the two most commonly used

determine the period of the trig function

use even/odd properties

the properties were going to need for this section are the even & odd properties: Sine of (negative theta) = negative Sine of theta; Cos of (negative theta) = Cos of theta; Tan of (negative theta) = negative Tan of theta

find the values of trigonometric functions

find the exact value of a trig function given a value & quadrant

find values of the trig functions using identities

Fundamental Identities: Csc of theta = 1/sin of theta; Sec of theta = 1/cos of theta; Cot of theta= 1/tan of theta; Cot of theta= cos of theta/sine of theta; Tan of theta= sine of theta/cos of theta

Subtopic

Section 6.5: Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

graph cosecant & secant function

graphing functions of the form y= A tan(wx) +B

graph function of the form y= A tan(wx)+B and y= cot (wx)+B

graph function of the form y= A tan(wx)+B and y=A cot (wx)+B

graph functions of the form y= A csc (wx) +B and y= A sec (wx)

Section 7.1: The Inverse of Sine, Cosine, and Tangent Functions

Subtopic

Section 7.3: Trigonometric Equations

Subtopic

Section 7.5: Sum & Difference Formulas

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