y = sin x solve (325,212.5) (425,150) (560, 200)

To solve the equation \( y = \sin(x) \) for the given points \((325, 212.5)\), \((425, 150)\), and \((560, 200)\), we need to check if these points satisfy the equation.

Let's analyze each point to see if it lies on the curve \( y = \sin(x) \).

### 1. Convert x-values to radians
Since the sine function generally operates in radians, let's convert the x-values to radians:
\[
x_{\text{radians}} = \frac{x_{\text{degrees}} \times \pi}{180}
\]

### 2. Calculate \( \sin(x) \) for each x-value
After converting, we will calculate \( \sin(x) \) and compare it to the given y-values.

### 3. Compare the calculated \( \sin(x) \) values to the given y-values

#### Step 1: Convert x-values to radians
- For \( x = 325^\circ \):
  \[
  x_{\text{radians}} = \frac{325 \times \pi}{180} \approx 5.672 \text{ radians}
  \]

- For \( x = 425^\circ \):
  \[
  x_{\text{radians}} = \frac{425 \times \pi}{180} \approx 7.418 \text{ radians}
  \]

- For \( x = 560^\circ \):
  \[
  x_{\text{radians}} = \frac{560 \times \pi}{180} \approx 9.777 \text{ radians}
  \]

#### Step 2: Calculate \( \sin(x) \)
- For \( x = 325^\circ \):
  \[
  \sin(325^\circ) \approx -0.0872
  \]

- For \( x = 425^\circ \):
  \[
  \sin(425^\circ) \approx 0.4226
  \]

- For \( x = 560^\circ \):
  \[
  \sin(560^\circ) \approx 0.4226
  \]

#### Step 3: Compare with given y-values
- Point \( (325, 212.5) \):
  \[
  \text{Given } y = 212

Learn how to solve the equation \( y = \sin(x) \) for the points (325, 212.5), (425, 150), and (560, 200) using trigonometric principles. Detailed analysis includes converting degrees to radians, calculating \( \sin(x) \), and verifying against given y-values.

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