Answer:
The quarter points are
pi /2,1
3 pi/4, 5
pi, 1
5 pi/4, -3
3 pi/2, 1
Step-by-step explanation:
We know that in
[tex]y = \sin(x) [/tex]
the coordinates are
0,0
pi/2,1
pi,0
3 pi/2,-1
2,0
Our function however is new which is
[tex]y = 4 \sin(2x - \pi) + 1[/tex]
Our amplitude is 4 so let multiply the y values by 4.
0,0
pi/2, 4
pi,0
3 pi/2, -4
2 pi,0
Our period is pi now. Remeber that for later.
Our phase shift is pi/2 now so we would move this to the right.
Add pi/2 to the x values.
- pi/2,0
- pi,4
- 3pi/2,0
- 2 pi , -4
- 5 pi/2, 0.
Translate the y values up 1.
pi/2,1
pi,5
3 pi/2, 1
2 pi,-3
5 pi/2, 1
The quarter points is the period divide by 4. the period is pi so
[tex] \frac{\pi}{4} [/tex]
Keep pi/2, 1 and add pi/4 to the x values and keep the y value.
- pi/2,1
- 3 pi/4, 5
- pi, 1
- 5 pi/4, -3
- 3 pi/2, 1
