The Period, Amplitude, Intercepts, And Values Of The Sine Function

f(x)=sinx

f'(x)=cosx

1. What is the period of the function?

The standard form of the sine function is f(x) = sin(x), and the period of the sine function is defined as the length of the smallest interval over which the function repeats itself. The period of the sine function is 2π, meaning that the sine of any angle has the same value as the sine of that angle plus any multiple of 2π.

2. What is the amplitude of the function?

The amplitude of the sine function is the distance from the midpoint of the function to its maximum or minimum value. Since the sine function oscillates between -1 and 1, its amplitude is 1.

3. What are the x-intercepts of the function?

The x-intercepts of the sine function occur at values of x for which sin(x) = 0. This happens when x is an integer multiple of π. Therefore, the x-intercepts of the function are π, 2π, 3π, etc.

4. What are the y-intercepts of the function?

The y-intercept of the sine function occurs at x = 0, where sin(0) = 0. Therefore, the y-intercept of the function is 0.

5. What are the maximum and minimum values of the function?

The sine function oscillates between the maximum value of 1 and the minimum value of -1. Therefore, the maximum value of the function is 1, and the minimum value of the function is -1.

6. What are the coordinates of the points of intersection between the graph of f(x) = sin(x) and the x-axis?

The points of intersection between the graph of f(x) = sin(x) and the x-axis are the x-intercepts of the function. These points have coordinates (π,0), (2π,0), (3π,0), etc.

7. What are the coordinates of the points of intersection between the graph of f(x) = sin(x) and the y-axis?

The points of intersection between the graph of f(x) = sin(x) and the y-axis occur at x = 0, where sin(0) = 0. Therefore, the point of intersection between the graph of f(x) = sin(x) and the y-axis is (0,0).

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