Math Problem Statement

graph für g(x) = 2 * sin(x) + 1 in centimeter

Solution

To create a graph of the function g(x)=2sin(x)+1g(x) = 2 \cdot \sin(x) + 1 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, sin(x)\sin(x), which oscillates between -1 and 1.
  • Scaling it by 2 gives 2sin(x)2 \cdot \sin(x), 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 2π2\pi, so the wave repeats every 2π2\pi 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: 2π2\pi 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:

  1. Would you like to explore how different scales on the x-axis affect the appearance of the graph?
  2. Should we consider negative x-values in this graph or just focus on positive ones?
  3. How does the vertical shift of 1 affect the graph compared to the standard sine function?
  4. Do you want to include specific points of interest (e.g., max, min, intercepts) on the graph?
  5. 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