Advanced Function Period 1

Tuesday, 8 November 2011

chapter 6.5 Making Connections

chapter 6.5 Making Connections

there are 3 application of log function :
1. pH scale http://www.elmhurst.edu/~chm/vchembook/184ph.html
2. Decibel scale http://hyperphysics.phy-astr.gsu.edu/hbase/sound/db.html
3. Richter scale http://www.sosmath.com/algebra/logs/log5/log56/log56.html

those are really good websites that help me to understand it. However, Ms. Joanne Ho did a pretty good work in explaining the applications. :)

chapter 6.4 Power Law of Log

chapter 6.4 Power Law of Log

http://www.es.ucl.ac.uk/undergrad/geomaths/level1/logsnb/MHlogsnbintro8.htm
this is a very good website for power law of log. really it helps alot to me while studying.
it pretty much covers the whole 6.4

simpler version of it
http://www.purplemath.com/modules/logrules.htm

i would like to end my post with a really great song :

Chapter 6.3 Transformation of Log Functions

Chapter 6.3 Transformation of Log Functions

y = a log (bx + c ) + d

a = vertically (stretch / compress )
b = horizontally (stretch / compress )
c = translate ( left / right )
d = translate ( up/ down )
*take a pen; write it down; as it will be a helpful tools in the future while dealing with transformation of log functions.

http://archives.math.utk.edu/visual.calculus/0/shifting.6/index.html

chapter 6.2 Logarithms

Logarithms.

First of all, i would like to share a pretty good link for people who wants to learn more about log and exponential function ( from the previous post).
http://www.themathpage.com/aprecalc/logarithmic-exponential-functions.htm

logarithms ?
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10³ = 10 × 10 × 10. More generally, if x = b^y, then y is the logarithm of x to base b, and is written log_b(x), so log₁₀(1000) = 3.

The picture shown is a basic formula for a log.

More over, i would like you all to visit the link that ive posted right after this paragraph to increase your understanding on logarithm; as it may be the hardest chapter if you didnt get it really well.
Links :

http://www.sosmath.com/algebra/logs/log4/log44/log44.html
http://www.chem.tamu.edu/class/fyp/mathrev/mr-log.html
http://webmath.amherst.edu/qcenter/logarithms/index.html

thanks :)

Advanced Function Chapter 6.1

Exponential and Its Inverse

exponential functions are useful for describing relationships.
for example, if growth of the population is proportional to the size of the population as it grows, we describe the growth as exponential

however i found a very interesting video of inversing an exponential function on youtube.

ive also found a pretty awesome website :

http://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htm

visit it as it will blow your mind so you dont have to worry about log anymore :)

Monday, 10 October 2011

Chapter 4.5(Prove Trigonometry Identities)

Pythagorean Identity

$\cos^2\theta + \sin^2\theta = 1\!$

Quotient Identities
$\tan\theta = \frac{\sin\theta}{\cos\theta}.$

Reciprocal Identities
$\sec\theta = \frac{1}{\cos\theta},\quad\csc\theta = \frac{1}{\sin\theta},\quad\cot\theta=\frac{1}{\tan\theta}=\frac{\cos\theta}{\sin\theta}.$

The last part of the chapter, proving trigonometry identities. above is some new formulas that quite useful for you to use as you are working on proving.

Chapter 4.4 ( Compound Angle Formulas )

The following are important trigonometric relationships:

sin(A + B) = sinAcosB + cosAsinB
cos(A + B) = cosAcosB - sinAsinB
tan(A + B) = tanA + tanB
1 - tanAtanB

sin(A - B) = sinAcosB - cosAsinB
cos(A - B) = cosAcosB + sinAsinB
tan(A - B) = tanA - tanB
1 + tanAtanB

Memorize all the formulas above and twist it around (depends on your creativity and the requirement from questions).