A machine produces a voltage in the following formula V(t) = 300cos(10(pi)x). X is the time in seconds. Graph the function with the restriction 0 < X < 1
To graph the function V(t) = 300cos(10πx), where x is the time in seconds, with the restriction 0 < x < 1, follow these steps:
Step 1: Determine the range of x values for the graph. In this case, the restriction states that x must be greater than 0 and less than 1. So, the graph will only show values of x within this range.
Step 2: Choose a suitable scale for the x- and y-axes on your graph. Since the restriction is from 0 to 1 for x, you can use a scale that accommodates this range. For the y-axis, examine the equation V(t) = 300cos(10πx) to determine the range of values. The cosine function produces values between -1 and 1, so a suitable scale for the y-axis would be from -300 to 300.
Step 3: Plot points on the graph based on the values of the equation V(t) = 300cos(10πx) for the given range of x. Start by selecting several points within the range 0 < x < 1, and calculate the corresponding values of V(t) using the equation. For example, when x = 0, V(t) = 300cos(10π*0) = 300cos(0) = 300. Similarly, find values of V(t) for other x values within the range.
Step 4: Connect the plotted points to form a smooth curve representing the function V(t) = 300cos(10πx) for 0 < x < 1.
By following these steps, you will be able to graph the given function V(t) = 300cos(10πx) with the specified restriction.