Question 470594: The function f is defined for 0 ≤ x ≤ 360, by  where a, b and c are positive integers. Given that amplitude of f is 2 and the period f is 120 degrees,
i) state the value of a and b.
Given further that the minimum value of f is -1.
ii) state the value of c,
iii) sketch the graph of f.
*Please answer as soon as possible and please explain how you sketch the graph bro :) =)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! f(x) = (a)sin(bx) + c
The function f is defined for 0 ≤ x ≤ 360, by where a, b and c are positive integers. Given that amplitude of f is 2 and the period f is 120 degrees,
i) state the value of a and b.
Given further that the minimum value of f is -1.
ii) state the value of c,
iii) sketch the graph of f.
**
Standard form for sin function: y=A sin(Bx-C), A=amplitude, period=2π/B, C/B=phase-shift
i) state the value of a and b
a=2 (given amplitude)
period=120º=360º/b
b=360/120=3
..
ii) state the value of c
c=phase-shift
no data given
also, given statement that minimum value of f is -1 is in conflict with amplitude=2. Sin function varies between ±2
..
iii) sketch the graph of f
period=120º
1/4 period=120/3=30º
assume no phase-shift
On the x-axis make tick marks at 0, 30º, 60º, 90º, and 120º
you now have the following points to plot the curve as follows:
(0,0), (30º,2), (60º,0), (90º,-2), (120º,0)
or in radians:(0,0), (π/6,2), (π/3,0), (π/2,-2), (2π/3,0)
see graph below:(sorry, could only show it in radians)
|
|
|
