We'Ve CoMe To An EnD aGaIn ??? =((( Oh WeLlL...

HEY MY FRIENDS AND ALSO MY DEAR TEACHER..SO IT SEEMS WE HAVE COME AGAIN TO AN END TO ME GUIDING YOU ALL IN ANOTHER CHAPTER OF ADVANCED FUNCTION. AND I KNOW I WILL NOT BE SEEING YOU ALL AGAIN IN THIS BLOG. NIWAYS, HOPE I HAVE HELPED YOU ALL IN SOME WAY TO UNDERSTAND SOME HARD PARTS OF ADVANCED FUNCTION. GUD LUCK FROM ME TO ALL OF YOU ALL IN YOUR STUDIES AND HOPE WE MIGHT MEET AGAIN IN ANOTHER BLOG NEXT TIME..BUBYE!! ~.~ :))

LaSt SuBtOpIc FoR tHiS cHaPtEr :D

HEY EVERYONE :) SO WE HAVE COME TO THE LAST SUBTOPIC OF THIS CHAPTER, THERE'S NOTHING MUCH THAT IS DIFFERENT IN THIS SUBTOPIC. WE STILL HAVE TO FIGURE THE VALUES OF ANGLE OF x. ONLY THIS TIME WE GET COMPLICATED EQUATIONS IN WHICH WE HAVE TO FACTORIZE OR SIMPLIFY TO GET THE VALUE sin x, tan x AND cos x. THE REST OF THE WORKING IS THE SAME AS LEARNED IN THE PREVIOUS SUBTOPIC. ONE OTHER THING IS THAT THE INSTANTANEOUS RATES OF CHANGE OF A SINUSOIDAL FUNCTION FOLLOW A SINUSOIDAL PATTERN.

LaSt SuBtOpIc FoR tHiS cHaPtEr :D

HEY EVERYONE :) SO WE HAVE COME TO THE LAST SUBTOPIC OF THIS CHAPTER, THERE'S NOTHING MUCH THAT IS DIFFERENT IN THIS SUBTOPIC. WE STILL HAVE TO FIGURE THE VALUES OF ANGLE OF x. ONLY THIS TIME WE GET COMPLICATED EQUATIONS IN WHICH WE HAVE TO FACTORIZE OR SIMPLIFY TO GET THE VALUE sin x, tan x AND cos x. THE REST OF THE WORKING IS THE SAME AS LEARNED IN THE PREVIOUS SUBTOPIC. ONE OTHER THING IS THAT THE INSTANTANEOUS RATES OF CHANGE OF A SINUSOIDAL FUNCTION FOLLOW A SINUSOIDAL PATTERN.

MaKiNg CoNnEcTiOnS aNd InStAnTaNeOuS rAtE oF cHaNgE :)

HEY GUYS, I KNOW THAT IT IS SUPRISING THAT I'M POSTING THIS VIDEO RIGHT NOW, AS IT IS ABOUT THE LAST SUBTOPIC IN THE CHAPTER WE'RE LEARNING NOW..MS JOANNE HAVNT TAUGHT US THIS SUBTOPIC YET..HOWEVER, AS I'M TOO FREE, I THOUGHT WHY NOT JUST POST THIS VIDEO FIRST HUH..MAYBE SOME OF YOU WANNA HAVE A LOOK AT IT TO GET SOME IDEA ON IT BEFORE WE LEARN MORE ABOUT IT IN CLASS..SO HAPPY WATCHING @ LEARNING GUYS :DDD

SoMeThInG fAmIlIaR?? yeAhHh..OnLy We'Ve LeArNeD iT iN dEgReE FoRm ^^

HEY EVERYONE, I'M BACK HERE AGAIN WITH YOU ALL AFTER A LONG AND BUSY WEEKEND. WELL, WE STUDIED ON HOW WE SHOULD SOLVE TRIGONOMETRIC EQUATIONS TODAY. IN A WAY,TODAY'S LESSON MIGHT BE REVIEW FOR MOST OF YA..CAUSE WE HAVE STUDIED THESE BEFORE..ONLY IN DEGREE FORM. HOWEVER, WE'RE LEARNING THROUGH RADIAN PROCESS RIGHT NOW..

THERE'S NOT MUCH FOR ME TO POINT OUT IN THIS CHAPTER. TRIGONOMETRIC EQUATIONS CAN BE SOLVED ALGEBRAICALLY BY HAND OR GRAPHICALLY WITH TECHNOLOGY. THEY ARE OFTEN MULTIPLE SOLUTIONS. MAKE SURE YOU FIND ALL SOLUTIONS ACCORDING TO THE GIVEN DOMAIN IN THE QUESTIONS. SOMETIMES, THE SOLUTION YOU GET MIGHT BE BIGGER OR SMALLER THAN THE GIVEN DOMAIN, SO MAKE SURE YOU DON'T INCLUDE THEM. AND ONE MORE THING IS, QUADRATIC TRIGONOMETRIC EQUATIONS CAN OFTEN BE SOLVED BY FACTORING.

SO TO FURTHER ENHANCE YOUR UNDERSTANDING ON THIS FAVORITE SUBTOPIC OF MINE IN THIS CHAPTER, I HAVE INCLUDED A VIDEO FOR YOUR VIEWING..CHEERS!! :)

AnD aFtEr 2 DaYs Of StUdYiNg AbOuT sInUsOiDaL fUnCtIoNs..HeRe YoU gO!!! :)

SO, WE WERE TAUGHT IN CLASS FOR 2 DAYS REGARDING THE 3RD SUBTOPIC OF THIS CHAPTER...SINUSOIDAL FUNCTIONS OF THE FORM f ( x ) = a sin [ k ( x - d ) ] + c AND f ( x ) = a cos [ k ( x - d ) ] + c...

ACTUALLY, THERE ISN'T MUCH TO REMEMBER IN THIS SUBTOPIC EXCEPT THE MEANINGS OF THE VARIABLE IN THE SINUSOIDAL FUNCTIONS..SO HERE ARE THE MEANINGS OF EACH VARIABLE..
|a| IS THE amplitude
d IS THE phase shift
c IS THE vertical translation
THE PERIOD OF A TRANSFORMED FUNCTION IS GIVEN BY 2π/k.

I'M ALSO INCLUDING A GRAPH ON THIS SUBTOPIC TO MAKE YOU ALL UNDERSTAND MORE ABOUT IT :)

GrApHs Of ReCiPrOcAl TrIgOnOmEtRiC fUnCtIoNs...

LeT's ExPlOrE tHrEe MoRe TrIgOnOmEtRiC fUnCtIoNs :D

TODAY, WE LEARN ABOUT 3 MORE TRIGONOMETRIC FUNCTIONS AND THEIR PROPERTIES. THESE GRAPHS ARE y = csc x, y = sec x, and y = cot x. THESE 3 GRAPHS ARE RECIPROCAL GRAPHS AND THEY ARE RELATED TO THE GRAPHS OF THE 3 PRIMARY TRIGONOMETRIC FUNCTIONS. THESE 3 GRAPHS ARE ALSO PERIODIC. NOW, I WOULD LIKE TO ATTACH EXAMPLES OF HOW THESE 3 RECIPROCAL GRAPH WOULD LOOK LIKE..

GRAPH OF y = csc x...

GRAPH OF y = sec x...

GRAPH OF y = cot x...

 NOW THAT YOU HAVE ALL SEEN HOW THESE 3 RECIPROCAL GRAPHS LOOK LIKE, THERE ARE SOME KEY FEATURES THAT WE SHOULD NOTE. RECIPROCCAL TRIGONOMETRIC FUNCTIONS ARE DIFFERENT FROM INVERSE TRIGONOMETRIC FUNCTIONS BECAUSE...
~ csc x MEANS 1/sin x WHILE sin^-1 x ASKS YOU TO FIND AN ANGLE THAT HAS A SINE RATIO EQUAL TO x
~ sec x MEANS 1/cos x WHILE cos^-1 x ASKS YOU TO FIND AN ANGLE THAT HAS A COSINE RATIO EQUAL TO x
~ cot x MEANS 1/tan x WHILE tan^-1 x ASKS YOU TO FIND AN ANGLE THAT HAS A TANGENT RATIO EQUAL TO x