We can find some of the solutions of 
sin(x) = 0.1
 graphically by graphing 
y = sin(x) and y = 
 .


Use the graph below to estimate some of the solutions. (Let 
−3𝜋 < x < 3𝜋.
 Enter your answers as a comma-separated list. Round your answers to four decimal places.)
x =

To estimate the solutions of the equation \( \sin(x) = 0.1 \) graphically, we can find where the graph of \( y = \sin(x) \) intersects the line \( y = 0.1 \) in the interval \( -3\pi < x < 3\pi \).

The sine function oscillates between -1 and 1, so we will look for the points where \( y = 0.1 \) intersects with the sine curve. 

**Steps to estimate solutions:**

1. **Identify the points of intersection**: You need to look at the graph to determine where the line \( y = 0.1 \) crosses the sine curve. 
2. **Determine the approximate x-values**: In the interval \( -3\pi \) to \( 3\pi \), you can find several intersections.

Using this method, the solutions (estimated from the graph) are approximately:

1. \( x \approx -3.0416 \)
2. \( x \approx -2.3020 \)
3. \( x \approx -0.1000 \)
4. \( x \approx 0.1000 \)
5. \( x \approx 2.3020 \)
6. \( x \approx 3.0416 \)

Thus, rounding these values to four decimal places, the solutions are:

\[
x \approx -3.0416, -2.3020, -0.1000, 0.1000, 2.3020, 3.0416
\]

**Final answer**: 
\(-3.0416, -2.3020, -0.1000, 0.1000, 2.3020, 3.0416\)

Would you like more details or have any questions? Here are some related questions:

1. How does the graph of \( y = \sin(x) \) behave over different intervals?
2. What is the general solution for \( \sin(x) = k \)?
3. Can you explain how to derive these solutions algebraically?
4. How would you find intersections for different values of \( k \)?
5. What are the properties of the sine function that affect its intersections with horizontal lines?

**Tip**: Always check the periodicity of the sine function to identify additional solutions beyond the given interval.

We can find some of the solutions of sin(x) = 0.1 graphically by graphing y = sin(x) and y = 0.1. Use the graph below to estimate some of the solutions. (Let −3π < x < 3π. Enter your answers as a comma-separated list. Round your answers to four decimal places.) x =

Estimate the solutions of the equation sin(x) = 0.1 graphically by identifying intersections in the interval -3π < x < 3π. Solutions include x ≈ -3.0416, -2.3020, -0.1000, 0.1000, 2.3020, and 3.0416, rounded to four decimal places. This problem highlights key trigonometric concepts.

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