Math Problem Statement

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

Solution

To solve the equation y=sin(x)y = \sin(x) for the given points (325,212.5)(325, 212.5), (425,150)(425, 150), and (560,200)(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)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: xradians=xdegrees×π180x_{\text{radians}} = \frac{x_{\text{degrees}} \times \pi}{180}

2. Calculate sin(x)\sin(x) for each x-value

After converting, we will calculate sin(x)\sin(x) and compare it to the given y-values.

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

Step 1: Convert x-values to radians

  • For x=325x = 325^\circ: xradians=325×π1805.672 radiansx_{\text{radians}} = \frac{325 \times \pi}{180} \approx 5.672 \text{ radians}

  • For x=425x = 425^\circ: xradians=425×π1807.418 radiansx_{\text{radians}} = \frac{425 \times \pi}{180} \approx 7.418 \text{ radians}

  • For x=560x = 560^\circ: xradians=560×π1809.777 radiansx_{\text{radians}} = \frac{560 \times \pi}{180} \approx 9.777 \text{ radians}

Step 2: Calculate sin(x)\sin(x)

  • For x=325x = 325^\circ: sin(325)0.0872\sin(325^\circ) \approx -0.0872

  • For x=425x = 425^\circ: sin(425)0.4226\sin(425^\circ) \approx 0.4226

  • For x=560x = 560^\circ: sin(560)0.4226\sin(560^\circ) \approx 0.4226

Step 3: Compare with given y-values

  • Point (325,212.5)(325, 212.5): [ \text{Given } y = 212

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine Function
Radians Conversion

Formulas

\( y = \sin(x) \)

Theorems

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Suitable Grade Level

Advanced High School