sketch one cycle of y=-3 sin 0
i know you guys wouldnt be able to draw it for me on here, but is this able to do on a graphing calculator, or could u explain the steps needed to do this problem?
thanks in advance
If you really mean sine of zero, it is 0 forever. However if you mean sine of theta let theta go from zero to 360 degrees or 2 pi radians
It will start out at 0 when theta = 0
it will be -3 at theta = pi/2 or 90 degrees
it will be zero at theta = pi or 180 degrees
it will be +3 at theta = 3 pi/2 or 270 degrees
it will be 0 when theta = 2 pi or 360 degrees.
You can also do in between points of course.
To sketch one cycle of the function y = -3sin(θ), you can use a graphing calculator or follow these steps manually:
1. Start by understanding the general shape of the sine function. The sine function oscillates between -1 and 1 in a smooth wave pattern.
2. Determine the period of the function. The period in this case is given by the value inside the sine function, which is 0. The period is usually denoted as 2π divided by the value inside the parentheses. So in this case, the period is 2π/0, which is undefined. This means that the function does not repeat itself as the input variable (θ) changes.
3. Since the period of the function is undefined, you can choose any range of values for θ to sketch one cycle. A common choice is to use a range of θ from 0 to 2π (or 0° to 360°).
4. Create a table of values. Choose several values of θ within the range you selected (e.g., 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4, 2π) and substitute them into the equation y = -3sin(θ) to find the corresponding y-values. Remember to use radians when working with trigonometric functions.
5. Plot the points obtained from the table on a graph, using the values of θ as the x-coordinates and the corresponding y-values as the y-coordinates.
6. Connect the points with a smooth curve to represent the waveform of the sine function. Since the coefficient in front of the sin function is -3, the amplitude of the graph will be stretched by a factor of 3.
If you're using a graphing calculator, follow these steps:
1. Enter the equation, y = -3sin(θ), into the calculator.
2. Set the calculator to radian mode to work with trigonometric functions.
3. Go to the graphing mode or function plotting mode on the calculator.
4. Set the window or range of the graph to include θ values from 0 to 2π.
5. Graph the equation on the calculator, and it will display one cycle of the graph.
Remember, specific instructions may vary based on the brand and model of your graphing calculator, so consult the user manual for more accurate guidelines.