How would you graph sin 4x = 1 ?
a) How do you find amplitude?
b) How do you find Period?
I'm kind of confused about the "=1" part.
Thanks :)
I am also confused. That is not the equation of a wave.
Could it be
L = sin 4 x ?
in that case the amplitude is 1
and the period is when 4 x = 2 pi
or x = pi/2
so period is pi/2
and this can be written
L = 1 sin 2 pi x/.5 pi
To graph the equation sin(4x) = 1, we need to understand how to find the amplitude, period, and then plot the graph accordingly.
a) Amplitude:
The amplitude of a sine function is the distance between the midline and the maximum/minimum point. In this case, since the equation is sin(4x) = 1, the amplitude is always positive and equal to 1. So the graph will oscillate between y = 1 and y = -1.
b) Period:
The period of a sine function represents the distance between two successive peaks or troughs of the graph. To find the period, we use the formula: Period (T) = 2π / |B|, where B is the coefficient of x inside the argument of the sine function. In this case, the coefficient is 4, so the period is T = 2π / |4| = π/2.
Now, to graph sin(4x) = 1 and understand what the "= 1" part means, consider that the sine function takes values between -1 and 1. So, for sin(4x) = 1, it means that the graph will intersect the value of y = 1 at certain x-values.
To plot the graph, you can follow these steps:
1. Mark the y-axis as the midline, which is the horizontal line at y = 0 (since the amplitude is 1).
2. Divide the x-axis into sections representing the period, which is π/2 in this case. Starting from x = 0, make ticks at intervals of π/2, π, 3π/2, etc.
3. Since sin(4x) = 1, the graph will intersect the midline at y = 1 at certain x-values. These x-values occur when 4x is equal to π/2, 5π/2, 9π/2, and so on. Solve for x by dividing these x-values by 4, which gives x = π/8, 5π/8, 9π/8, etc. Mark these points on the graph.
4. Repeat step 3 for all the successive peaks of the sine curve. Since the period is π/2, the next peaks will occur at x = 3π/8, 7π/8, 11π/8, etc.
5. Connect the plotted points with a smooth curve to complete the graph.
Remember, sin(4x) = 1 represents a periodic function, so the graph will repeat itself after each period.
I hope this explanation helps you understand how to graph the equation sin(4x) = 1 and how to find the amplitude and period. If you have any further questions, feel free to ask!