how to graph y= sin2(x+1) and y =cos 10(x+3)
I know how to find amplitude period phase shift and Vertical shift
for first question amp=1 period =pie
phase shift =left 1
how to find points to plot it?
what values we should put for x interms pies or numbers that is confusing me
I will let you play around with
http://www.wolframalpha.com/input/?i=y%3D+sin%282%28x%2B1%29%29
remember x is in radians, also notice the extra set of brackets I put in.
What happens when we enter it as you typed it ?
try y = cos(5(x - 3)) + 2
ignore the fancy math at the bottom of the page
To graph the functions y = sin(2(x + 1)) and y = cos(10(x + 3)), you can start by determining the key points on the graph. Here's how you can find these points:
1. Determine the period: In the case of y = sin(2(x + 1)), the period can be calculated as 2π/2 = π. Similarly, for y = cos(10(x + 3)), the period is 2π/10 = π/5.
2. Find the phase shift: For y = sin(2(x + 1)), the phase shift is -1 (since it is x + 1 = 0). For y = cos(10(x + 3)), the phase shift is -3 (x + 3 = 0).
3. Determine the amplitude: The amplitude of both functions is 1, which means the graph oscillates between -1 and 1.
4. Find the vertical shift: Both functions don't have any vertical shifts, so the graphs start at the origin (0, 0).
Now, let's plot some key points for each function:
For y = sin(2(x + 1)):
- Start at the phase shift: (-1, 0)
- Go to the right by the period (π): (0, 0)
- Go to the right by another π: (π, 0)
- Go to the right by another π: (2π, 0)
- Continue this pattern to plot more points.
For y = cos(10(x + 3)):
- Start at the phase shift: (-3, 1)
- Go to the right by the period (π/5): (-2.8, 1)
- Go to the right by another π/5: (-2.6, 1)
- Go to the right by another π/5: (-2.4, 1)
- Continue this pattern to plot more points.
Remember, on the x-axis, you can use multiples of the period (π) or decimal values between the multiples. These points will help you sketch the graph accurately.