Given the minimum and maximum values of the function y=3sin(x). My anser is -3 for min and 3 foe max by looking at the graph on my calculator. I want to know how solve for it on paper without looking at the graph.
sin is max at π/2 , and min at 3π/2
To find the minimum and maximum values of the function y = 3sin(x) without using a graph, you can analyze the properties of the sine function.
1. Start by recalling the range of the sine function. The sine function oscillates between -1 and 1. So, for the function y = 3sin(x), the range will be between -3 and 3.
2. To find the minimum and maximum values within this range, consider the fact that the amplitude of the sine function is 1. In this case, the amplitude is multiplied by 3, so the maximum value of y will be 3, and the minimum value will be -3.
Therefore, based on analyzing the properties of the sin function, the minimum value of y = 3sin(x) is -3, and the maximum value is 3.
To find the minimum and maximum values of the function y = 3sin(x) without relying on a graph, you can use your knowledge of the properties of the sine function.
The sine function oscillates between -1 and 1 as x varies from -∞ to +∞. Since the given function is y = 3sin(x), the amplitude is multiplied by 3, which means the function oscillates between -3 and 3.
To determine the minimum and maximum values of the function, you need to identify the intervals on the x-axis where the function reaches these extreme values.
The maximum value of the function occurs when the sine function is at its peak, which is at x = π/2. Plugging this value into the equation y = 3sin(x), we get y = 3sin(π/2) = 3.
The minimum value of the function occurs when the sine function is at its trough, which is at x = 3π/2. Plugging this value into the equation y = 3sin(x), we get y = 3sin(3π/2) = -3.
Therefore, the maximum value (or peak) of the function y = 3sin(x) is 3, and the minimum value (or trough) is -3, confirming your observation from the graph.