How do I graph sin and cosin
example: graph y=-4sin(x + 3.14)
Your function is the sin function shifted by pi units to the left.
You need to study the sin function and know how to graph it. There should be a picture of it in your text, it's a very commonly used funtion that has a wave pattern.
To graph the function y = -4sin(x + 3.14), follow these steps:
1. Determine the amplitude: The amplitude of the function is the absolute value of the coefficient in front of the sin function. In this case, the amplitude is |-4| = 4. This means the graph will oscillate between -4 and 4 on the y-axis.
2. Determine the period: The period of the sine function is 2π. When the argument (x + 3.14) inside the sin function is increased by 2π, the graph completes one full cycle. Therefore, the period of this function is 2π.
3. Find the phase shift: The phase shift is the horizontal shift of the graph. In this case, the argument (x + 3.14) inside the sin function is shifted to the left by 3.14 units. This means the graph is shifted to the right by 3.14 units.
4. Plot key points: To plot the graph, you can choose specific values of x and find the corresponding y values using the function.
- Let's start with x = -3.14 (since the phase shift is -3.14):
When x = -3.14, the argument becomes (-3.14 + 3.14) = 0.
Plug it into the function: y = -4sin(0) = 0.
So, one key point is (-3.14, 0).
- Next, choose other values for x such as -6.28, -9.42, -12.56, etc., and find the corresponding values of y by evaluating the function.
5. Graph the points: Plot the key points on the coordinate plane, using the values of x and y you found. Connect the points with a smooth curve to complete the graph.
Remember, the graph will oscillate between -4 and 4, with a period of 2π, and will be shifted to the right by 3.14 units.