on the same set of axes sketch the graph of f(x)=sin2x and g(x)=2sin x for x (o,180 degrees)
To sketch the graphs of the functions f(x) = sin(2x) and g(x) = 2sin(x) on the same set of axes for x values between 0 and 180 degrees, you can follow these steps:
Step 1: Determine the x-values at regular intervals. In this case, let's choose increments of 30 degrees (0°, 30°, 60°, 90°, 120°, 150°, and 180°).
Step 2: Calculate the corresponding y-values for each function. Plug in each x-value into the respective function to find the y-value. For example, for sin(2x), multiply the x-value by 2 before taking the sine, and for 2sin(x), multiply the sine of x by 2.
Step 3: Plot the points on the graph paper. For each (x, y) value pair, locate the x-value on the x-axis and the y-value on the y-axis. Mark the points accordingly.
Step 4: Connect the points. Draw smooth curves through the plotted points to form the shape of each function. For sin(2x), the curve will show more oscillations since the frequency is doubled (compared to sin(x)). For 2sin(x), the amplitude will be twice as large as a typical sine curve.
Step 5: Label the axes and add any necessary additional information, such as function labels or a key.
It is important to note that as a text-based AI, I cannot physically sketch the graph for you, but I hope the steps provided will guide you in accurately sketching the graph of the given functions on the same set of axes.