~ THE END ~

I guess that's all for chapter5! Im finally done with my blog! HOOORAYY=)) but remember guys, keep on practising to be excellent in this chapter.. afterall, practise makes permanent!



5.5 Making Connections and Instantaneous Rate of Change

The instantaneous rates of change of a sinusoidal function follow a sinusoidal pattern, and usually undrgoes transformation when modelling real-world processes.

Here's a simple video illustrating this subtopic :) Enjoy!=D

5.4 Solve Trigonometric Equations

1.Trigonometric equations can be solved in two ways:

• algebraically by hand
• graphically with technology

2. There are often multiple solutions. So, be sure to find all solutions that lie in the domain of interest.
3. Quadratic trigonometric ewuations can usually be solved by factoring.

Here are some interesting videos on solving trigonometric equations:) It's very beneficial..hope you guys gain the best of it! Have fun watching!:)

Solving Algebraically

Solving Graphically

LOVEEE MATHS! hehe:)

General Idea of 5.3

• The transformation of a sine/ cosine function f(x) to g(x) has the general form g(x) = a f [k(x-d)] + c, where |a| is the amplitude, d is the phase shift, and c is the vertical translation.
• The period of the transfored function is given by

5.3 Sinusoidal Functions of the form f(x) = a sin [ k(x-d) ] + c & f(x) = a cos [ k(x-d) ] + c

  f(x) = a sin [ k(x-d) ] + c 
  f(x) = a cos [ k(x-d) ] + c

a = amplitude
k-value = 2 / Period
d = phase shift to left / right
c = vertical translation upwards / downwards

EG:

y = sin x

y = 5 sin x ( where An =5)

y = sin x + 1

Maths Jokes (hahaha!! :P)

If only maths was as simple as this:

5.2 Graphs of Reciprocal Trigonometric Functions

Domain = {x Є R | x ≠ kx } , whereby k is an integer.

Range = { y > 1 or y < -1 }

Period = 2π

Vertical Asymptotes = x = kx , whereby k is an integer

Domain = {x Є R | x ≠ (2kx+1)(π/2) } , whereby k is an integer.

Range = { y > 1 or y < -1 }

Period = 2π

Vertical Asymptotes = x = (2kx+1)(π/2) ‘ whereby k is an integer

Domain = {x Є R | x ≠ kπ } , whereby k is an integer.

Range = { -1< y < 1 }

Period = π

Vertical Asymptotes = x = kx , whereby k is an integer

5.1 Graphs of Sine, Cosine, and Tangent Functions

here's an interesting song! haha:) it's quite entertaining! Well, that is the primary trigonometry identities: [SOH,CAH,TOA]
Sin x = Opposite / Hypotenuse
Cos x = Adjacent / Hypotenuse
Tan x = Opposite / Adjacent

• Basic graphs of trigonometric functions are:

Sine Graph

Cosine Graph

Tangent Graph

• Graphs y = sin x, y = cos x, y = tan x are periodic.

 

Original Graph	y = sin x	y = cos x	y = tan x
+ vertical translation v  Moves upward/downwards by c units	y = sin x + c	y = cos x + c
+ amplitude v  Amplitude increases/decreases by a factor	y = a sin x	y = a cos x	No amplitude because there is no max/min value
+ phase shift v  Shifts by d units to the left/right	y = sin (x-d)	y = cos (x-d)
+ period (k-value) v  Number of cycles in one period	y = sin kx	y = cos kx	π

Chapter 5 : TRIGONOMETRIC FUNCTIONS

Okay, now its time to update my blog again!:) This time, i'll be focussing on Chap5, trigonometric functions, one of the most interesting topics in advanced functions. I'm not being sarcastic here, really, trigo is indeed very interesting and mind-boggling. The satisfaction of solving a complex trigo question with a full-page answer is indescribable! Trust me, the feeling of accomplishment is the same as drinking a cup of hot chocolate with tiger biscuits, on a rainy day!:) it feels so g-o-o-d :) that is why I enjoy this chapter very much! Before I start off with the syllabus, let me enlighten you guys with some interesting maths facts, just as a warm up!=D

Did you know that??

1)      π=3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 ...

2)      A sphere has two sides. However, there are one-sided surfaces.

3)      In a group of 23 people, at least two have the same birthday with the probability greater than 1/2

4)      Among all shapes with the same perimeter a circle has the largest area.

5)      Among all shapes with the same area circle has the shortest perimeter.

6)      As in philosophy, there are transcendental numbers

7)      As in the art, there are imaginary and surreal numbers

8)      You are wrong if you think Mathematics is not fun

9)      Trigonometry aside, Mathematics comprises fields like Game Theory, Braids Theory, Knot Theory and more

10)   The next sentence is true but you must not believe it.

11)   The previous sentence was false.

12)   One can cut a pie into 8 pieces with three movements.

13)   The only triangle with rational sides and angles is equilateral.

14)   0!=1

15)   At any given time in New York there live at least two people with the same number of hairs.

Life is All about Maths!

If people don't believe that mathematics is simple, it is only because they do not realize how complicated life is. ~ =)