ThE bEgInNnINg Of ChApTeR 5 :)

SO HAVE STARTED CHAPTER 5 AT LAST. THE FIRST SUBTOPIC IN THIS CHAPTER IS GRAPHS OF SINE, COSINE AND TANGENT FUNCTIONS. FIRST OF ALL, LET ME ATTACH IMAGES OF GRAPH y = sin x, y = cos x and y = tan x FOR YOUR BETTER UNDERSTANDING..

GRAPH OF y = sin x

GRAPH OF y = cos x

GRAPH OF y = tan x

KEY POINTS OF THIS SUBTOPIC : -
~ THE GRAPHS OF y = sin x, y= cos x, and y = tan x ARE PERIODIC.
~ THE GRAPHS OF y = sin x AND y = cos x ARE SIMILAR IN SHAPE AND HAVE AN AMPLITUDE OF 1 AND A PERIOD OF 2π.
~ THE GRAPH OF y =sin x CAN BE TRANSFORMED INTO GRAPHS MODELLED BY EQUATIONS OF THE FORM y = sin x + c, y = a sin x, y = sin ( x - d ), and y = sin k x.
~ SIMILARLY, THE GRAPH OF y = cos x CAN BE TRANSFORMED INTO GRAPHS MODELLED BY EQUATIONS OF THE FORM y = cos x + c, y = a cos x, y = cos ( x - d ) and y = cos k x.
~ THE GRAPH OF y = tan x HAS NO AMPLITUDE BECAUSE IT HAS NO MAXIMUM OR MINIMUM VALUE. IT IS UNDEFINED AT VALUES OF x THAT ARE ODD MULTIPLES OF π/2, SUCH AS π/2 AND 3π/2. THE GRAPH BECOMES ASYMPTOTIC AS THE ANGLE APPROACHES THESE VALUES FROM THE LEFT AND THE RIGHT. THE PERIOD OF THE FUNCTION IS π.