Sinusoidals

Sinusoidals

-a function which can be written in the form of f(x)= asin(bx+c)+d or
f(x)= acos(bx+c)+d where a,b,c & d are real nos.

There are formulas to get the value of the ff so u can easily graph the equation:
(let's just pretend that # is a pie sign and [ ] is an absolute value except for the Range)

Period: 2#/[b] or 2pie over absolute value of b

Amplitude: [a] or abs value of a

Phase Shift: -c/b

Maximum: d + [a]

Minimum: d - [a]

Range: (d + [a], d - [a])

let's have a 1st ex:
Sketch: y=sin4x

1st thing to do is: label a,b,c,d
a = 1(coefficient of sin)
b = 4(coefficient of x)
c=0 }
d=0 } there's no c & d at this given equation

...to get the period, use the formula that i gave u..

Period= 2#/[b] = 2#/[4]= #/2

as well as the other ones..

Amplitude = [a] = [1] = 1

Phase Shift = -c/b = -(0)/4 = 0

Max = d + [a] =0 + [1] = 1

Min = d - [a] =0 - [1] = -1

so the Range will be: [-1,1]

here is another ex:

Sketch: y=cos(O - #/2)

a=1

b=1
c=-#/2

d=0

Period: 2#/[b] = 2#/[1]= 2#

Amplitude: [a] = [1] = 1

Phase Shift: -c/b = -(-#)/2 = #/2

Max: d + [a] = 0 + [1] = 1

Min: d - [a] = 0 - [1] = -1

Range: [-1, 1]

Sorry about the blog im really not good in making one. I was really having a hard time doing this and to explain it as well..so yah guys just try to understand it.