Question

Function: -\pi)+1" align="absmiddle" class="latex-formula">
Quarter Points of $y=sin(x)$: $(0,0)$ $(\frac{\pi}{2} ,1)$ $(\pi,0)$ $(\frac{3\pi}{2},-1)$ $(2\pi,0)$


Using the coordinates of the five quarter points of y = sin x to determine the corresponding quarter points on the graph of the function above.

Answer 1

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

$y = \sin(x)$

the coordinates are

0,0

pi/2,1

pi,0

3 pi/2,-1

2,0

Our function however is new which is

$y = 4 \sin(2x - \pi) + 1$

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

$\frac{\pi}{4}$

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