on the same set of axes: (0 degrees is greater than or equal to x and x is less than or equal to 360 degrees)
(a) sketch the graphs of y= sin degrees ,y=2sinx degrees and y=sin2x degrees
I would assume you know how to sketch
y = sinx
for y = 2 sinx, your amplitude is now 2 instead of 1
for y = sin 2x, amplitude is 1, but you will have 2 complete sine curves from 0 to 360
To sketch the graphs of these three trigonometric functions, namely y = sin(x) degrees, y = 2sin(x) degrees, and y = sin(2x) degrees, we will follow a step-by-step approach. Please note that in the following explanation, I will use the term "degrees" to specify the unit of measurement for angles.
Step 1: Create an x-axis and a y-axis on a graph paper, or you may use any graphing software of your choice.
Step 2: Determine the range of x-values based on the given condition: 0 degrees ≤ x ≤ 360 degrees. This means we need to draw the graph for all the possible angles within this range.
Step 3: Graphing y = sin(x) degrees:
- Start with x = 0 degrees. Calculate sin(0) using a scientific calculator or a trigonometric table. The value of sin(0) is 0. Plot this point on the graph at (0, 0).
- Move to x = 90 degrees. Calculate sin(90). The value of sin(90 degrees) is 1. Plot this point at (90, 1).
- Repeat this step for x = 180 degrees, x = 270 degrees, and x = 360 degrees while calculating the corresponding sin values and plotting the points.
- Connect these points using a smooth curve. The resulting graph should be a wave-like curve that oscillates between -1 and 1 along the y-axis.
Step 4: Graphing y = 2sin(x) degrees:
- Multiply the y-values of the previous graph (y = sin(x) degrees) by 2. This will stretch the curve vertically. For example, if the y-value for sin(x) is 0.5, for y = 2sin(x), the corresponding y-value would be 2 * 0.5 = 1.
- Repeat the same steps from Step 3, using the new calculated values to plot the points on the graph.
- Connect these points with a smooth curve. The resulting graph should exhibit a more pronounced wave-like pattern that oscillates between -2 and 2 along the y-axis.
Step 5: Graphing y = sin(2x) degrees:
- Multiply the x-values from the original graph (y = sin(x) degrees) by 2. This will compress the curve horizontally. For example, if the x-value for sin(x) is 30 degrees, for y = sin(2x), the corresponding x-value would be 2 * 30 = 60 degrees.
- Repeat the same steps from Step 3, using the new calculated x-values and original y-values to plot the points on the graph.
- Connect these points with a smooth curve. The resulting graph should exhibit a more compact wave-like pattern that oscillates between -1 and 1 along the y-axis.
By following these steps, you should be able to sketch the graphs of y = sin(x) degrees, y = 2sin(x) degrees, and y = sin(2x) degrees on the same set of axes.