What is the y - coordinate of the point at which the graph of y = 2 sin x - cos 2 x intersects the y - axis ?

Options

A. `-2`
B. `-1`
C. 0
D. 1

Explanation

To find the y-coordinate of the point at which the graph of \( y = 2 \sin x - \cos 2x \) intersects the y-axis, we need to evaluate the function at \( x = 0 \).

### Step-by-step Solution:

1. **Identify the function**: The function given is
\[ y = 2 \sin x - \cos 2x \]

2. **Substitute \( x = 0 \)**: To find the y-intercept, we substitute \( x = 0 \) into the function:
\[ y = 2 \sin(0) - \cos(2 \cdot 0) \]

3. **Calculate \( \sin(0) \)**: We know that
\[ \sin(0) = 0 \]
Therefore,
\[ 2 \sin(0) = 2 \cdot 0 = 0 \]

4. **Calculate \( \cos(0) \)**: We also know that
\[ \cos(0) = 1 \]
Thus,
\[ \cos(2 \cdot 0) = \cos(0) = 1 \]

5. **Combine the results**: Now substituting back into the equation:
\[ y = 0 - 1 = -1 \]

6. **Conclusion**: The y-coordinate of the point at which the graph intersects the y-axis is
\[ \boxed{-1} \]