I need a graph for y = 3 - 4cos pi/5(x - 1)
Not sure what the question is. You could plot it manually or use plotting software like Excel.
The period is 2π/(π/4) = 8
on the x-axis mark off 8 units, and split that into 4 equal parts.
draw an outline of a standard cosine curve using those divisions with an amplitude of 4
Now draw the reflection of your first curve in the x-asis
At this point you have y = -cos (π/5)x
no shift that last curve 1 unit to the right
you now have y = -cos π/5(x-1)
finally raise this curve up 3 units to get your final graph.
You might want to complete the curve to go from 0 to 9
In google type "functions graphs online"
When you see list of results click on:
rechneronline.de/function-graphs/
When page be open type your function and click option Draw
To graph the equation y = 3 - 4cos(π/5)(x - 1), we can follow a few steps:
Step 1: Determine the period
The period of the cosine function is 2π divided by its coefficient inside the parentheses, in this case, π/5. Therefore, the period is 2π / (π/5) = 10.
Step 2: Find the amplitude
The amplitude of the cosine function is the absolute value of the coefficient in front of the cosine function, in this case, 4.
Step 3: Determine the phase shift
The phase shift represents a horizontal shift of the graph. It is calculated by taking x - the value inside the parentheses and setting it equal to zero. In this case, x - 1 = 0, so the phase shift is 1 unit to the right.
Step 4: Identify key points and graph
To graph the equation, we can choose some key points, calculate their corresponding y-values, and plot them on the coordinate plane.
Let's choose x-values of -4, -2, 0, 2, and 4.
When x = -4: y = 3 - 4cos(π/5)(-4 - 1) = 3 - 4cos(-9π/5)
When x = -2: y = 3 - 4cos(π/5)(-2 - 1) = 3 - 4cos(-7π/5)
When x = 0: y = 3 - 4cos(π/5)(0 - 1) = 3 - 4cos(-π/5)
When x = 2: y = 3 - 4cos(π/5)(2 - 1) = 3 - 4cos(π/5)
When x = 4: y = 3 - 4cos(π/5)(4 - 1) = 3 - 4cos(3π/5)
Now, calculate the y-values for these x-values to plot the key points.
Using a graphing calculator or software, plot these points and connect them smoothly to form the graph of y = 3 - 4cos(π/5)(x - 1).