Week 5 Graphs of Sine and Cosine Functions

Week 5

Domain: All Real Numbers.

Range: [1; 1]

Period: P = 2

Quarter Period: 2 =4 = =2.

The Fundamental Cycle: [0; 2 ]

Symmetry: The graph of y = cos x is symmetric about the y-axis. The

function y = cos x is an even function. That is, cos(x) = cos x.

Changes in Amplitude

Multiplying a function by a positive number a will stretch the graph verti-

cally if a > 1 and compress the graph vertically if 0 < a < 1.

Domain: All Real Numbers.

Range: [1; 1]

Period: P = 2

Quarter Period: 2 =4 = =2.

The Fundamental Cycle: [0; 2 ]

Symmetry: The graph of y = sin x is symmetric about the origin. The

function y = sin x is an odd function. That is, sin(x) =  sin x

Learned from Khan Academy  

(I missed a few days of Math had to get caught up)

Find the Amplitude.... 

What is the Amplitude...?

The Amplitude of y= a sin x and y= a cos x represents half the distance between the maximum and minimum values of the function and is given by 

Amplitude=Absolute Value of "a"

Then find the period....

What is the period...?

The period is 2p(pie)/b equations y=a sin bx and y= a cos bx is given by Period 2p/b

Khan Academy helped me tremendously I didn't know how to do anything. It has now caught me up with my class. #Psyched  

Week 4 Trigonometric Functions of Any Angle

Week 4

Acute angles in standard position are all in the first quadrant, and all of their trigonometric functions exist and are positive in value. This is not necessarily true of angles in general. Some of the six trigonometric functions of quadrantal angles are undefined, and some of the six trigonometric functions have negative values, depending on the size of the angle. Angles in standard position have their terminal side in or between one of the four quadrants. 

When trying to find the angles you have to use the inverse of Sine Cosine and Tangent

This week was a little harder than week 3 the concept was harder to grasp with Khan Academy's videos I can gain a full understanding of this Concept overtime. 

Week 3 Right Triangle Trigonometry

Week 3

I have never understood Sine Cosine or Tangent

Soh Cah Toa

After taking geometry in 8th grade I prayed I wouldn't meet these again but in Chapter 4 I had no choice

With the help of Khan Academy I understand this concept 100%

Trying to find the measure of side X....?

Opposite= Y

Adjacent= 5 

The side opposite to the 30 degree angle is 1/2 the length of the hypotenuse

I would use Tangent because it is opposite over adjacent 

(TOA o stands for opposite and a stands for Adjacent)

After this week we didn't do much with triangle trigonometry but looking at the videos each week refreshes my memory on that concept 

This week was more of a laid back week because the videos from my Khan academy app explained everything slowly allowing me to understand the concept better. 

Week 2 The unit Circle

Week 2

Angle	Sin	Cos	Tan=Sin/Cos
30°			1/√3 = √3/3
45°			1
60°			√3

How To Remember?

To help you remember, think "1,2,3" :

• sin(30°) = ^√1/₂ = ¹/₂ (because √1 = 1)
• sin(45°) = ^√2/₂
• sin(60°) = ^√3/₂

And cos goes "3,2,1"

• cos(30°) = ^√3/₂
• cos(45°) = ^√2/₂
• cos(60°) = ^√1/₂ = ¹/₂ (because √1 = 1)

Soh Cah Toa

 Cosine is equal to the x coordinate where this radius intersects the Unit circle

The Sine is equal to the y coordinate where the coordinate  intersects the unit circle

y

Now, in this same circle, let us draw a right triangle 

θ

θ rad.

P = (x, y)

•

y

x

1

Using the right triangle definitions of the trigonometric functions

we can write

sin θ =

opposite

hypotenuse

= y,

and

cos θ =

adjacent

hypotenuse

= x.

This week I was a little puzzled with what my teacher threw at me..... "THE UNIT CIRCLE"
The unit circle is a tricky concept to grasp but with Khan Academy's continuous assistance I am understanding the Unit Circle better and better each day 

Khan Academy Trigonometry

5 week Recap of Khan AcademyTrigonometry

Introduction

I decided to use Khan Academy Trigonometry app because this app has everything relating  to Trigonometry.  It has 32 videos for Trigonometry understandings

 Week 1

This week we refreshed our memories on Sine Cosine Tangent Cotangent Secant Cosecant

Sin, Cos and Tan

A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question.
In any right angled triangle, for any angle:

The sine of the angle = the length of the opposite side
                                   the length of the hypotenuse

The cosine of the angle = the length of the adjacent side
                                      the length of the hypotenuse

The tangent of the angle = the length of the opposite side
                                      the length of the adjacent side

So in shorthand notation:
sin = o/h   cos = a/h   tan = o/a
Often remembered by: soh cah toa

Example

Find the length of side x in the diagram below:

The angle is 60 degrees. We are given the hypotenuse and need to find the adjacent side. This formula which connects these three is:
cos(angle) = adjacent / hypotenuse
therefore, cos60 = x / 13
therefore, x = 13 × cos60 = 6.5
therefore the length of side x is 6.5cm.

 The videos refreshes my memory and continues to keep the concept in my mind .



Khan Academy Topic: Trigonometry

Khan Academy Trigonometry is by far the best trigonometry app in the market. It has every topic about Trig you just have to select the page and it will show you a full length video explaining the topic you selected.

The unit circle has a fool description video on the unit circle











  Has a video on Revos which appeared in my last nights homework

Math.Trig BRO

A Triangle Solver that has a regular triangle solver as well as a right triangle solver.

Regular Triangle -

Enter one of the following and hit Calculate:

2 sides and an angle

2 angles and a side

3 sides

Right Triangle -

Enter one of the following and hit Calculate:

2 sides a  side of an angle

Math Trig works when you're trying to find out a triangles side or angle  for example on the triangle on the left i plugged in  90 degrees and sides 3 and 4 then i clicked calculate and it gives you the other side and the other two angles.

SDpro Math

Never heard of SDPro Math This amazing app keeps you on your game. You need recap after class or even a study tool to pass...?
SDPro Math gives you short quizzes on topics that you may struggle with.

Step

First you choice your subject

Then you choice your game mode Fun, Challenge or 2 player

Then you answer quiz (usually 35) that they give you 

Sometimes the game may be timed depending on the game mode

I picked Trigonometry and clicked One Player Challenge and this is question 3 of 10 the little 50/50 box narrows your answer down to 2 choices if you're having difficulty. The Cos of 90 degrees is 0 each answer has an explanation for why its that answer.

TRIG PRO FOR PRE-CALC FO SHOW

This unique app also computes the reference angle in degrees or radians for any given angle. Useful in real life for most people? No. Useful for Trig students? For sure Yo.

"Trig Pro" also includes:

- A unit circle in vivid colors

- Unit circle representations of the six trig functions

- A triangle solver (SSS, SAS, AAS, ASA, SSA)

- A solver for showing attributes and graphical representations of the six trig functions

- An extensive list of formulas and identities

- Degree/Radian converters

- A section on 30-60-90 and 45-45-90 triangles

- Examples of solving inverse trig problems

Example 1

Triangle with sides  measuring 5, 8, and 10 when you go to the Side Side Side (SSS) helper you plug in the side lengths and  click Solve Triangle and it will give you all 3 measures of the  angles

Add caption

Example 2

If you ever forget what the formula to find the opposite angle or side you can click on the Sin Cos Tan Csc Sec Cot helper and it will be sure to remind you