Math Problem Statement
graph für g(x) = 2 * sin(x) + 1 in centimeter
Solution
To create a graph of the function and ensure that measurements are in centimeters, we need to establish the scale in terms of centimeters along both the x-axis (horizontal) and y-axis (vertical). Let's break it down:
Function breakdown:
- The basic function is a sine wave, , which oscillates between -1 and 1.
- Scaling it by 2 gives , which oscillates between -2 and 2.
- Adding 1 shifts the entire graph vertically, so the function now oscillates between -1 and 3.
- The period of the sine function is , so the wave repeats every units (approximately 6.28 units along the x-axis).
Converting to centimeters:
- Let’s assume a reasonable scale for graphing:
- For the x-axis: You could assign 1 cm to correspond to 1 radian (or smaller, if you want more precision).
- For the y-axis: You could assign 1 cm to represent 1 unit, meaning the graph will span from -1 cm to 3 cm vertically.
Graph details:
- Range of the function: From -1 to 3.
- Period: or approximately 6.28 units, meaning the graph will repeat after every 6.28 cm on the x-axis.
Would you like me to generate this graph, or would you like a more detailed explanation on any part of the process?
Here are 5 questions to explore this further:
- Would you like to explore how different scales on the x-axis affect the appearance of the graph?
- Should we consider negative x-values in this graph or just focus on positive ones?
- How does the vertical shift of 1 affect the graph compared to the standard sine function?
- Do you want to include specific points of interest (e.g., max, min, intercepts) on the graph?
- How would adjusting the amplitude or frequency change the graph?
Tip: When graphing trigonometric functions, always consider the period, amplitude, and any phase or vertical shifts to ensure your graph accurately represents the function.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Graphing
Sine Function
Formulas
g(x) = 2 * sin(x) + 1
Period of sine function = 2π
Amplitude = 2
Vertical shift = 1
Theorems
Sine wave properties
Amplitude and period in sinusoidal functions
Suitable Grade Level
Grades 10-12