Draw the graph of `y=sin x ` and `y=cosx, 0 le x le 2pi`

Answer

To draw the graphs of \( y = \sin x \) and \( y = \cos x \) for the interval \( 0 \leq x \leq 2\pi \), we can follow these steps:

### Step 1: Identify Key Points for \( y = \sin x \)

1. **At \( x = 0 \)**:
\[ y = \sin(0) = 0 \]
2. **At \( x = \frac{\pi}{2} \)**:
\[ y = \sin\left(\frac{\pi}{2}\right) = 1 \]
3. **At \( x = \pi \)**:
\[ y = \sin(\pi) = 0 \]
4. **At \( x = \frac{3\pi}{2} \)**:
\[ y = \sin\left(\frac{3\pi}{2}\right) = -1 \]
5. **At \( x = 2\pi \)**:
\[ y = \sin(2\pi) = 0 \]

### Step 2: Plot the Points for \( y = \sin x \)

- The points to plot are:
- \( (0, 0) \)
- \( \left(\frac{\pi}{2}, 1\right) \)
- \( (\pi, 0) \)
- \( \left(\frac{3\pi}{2}, -1\right) \)
- \( (2\pi, 0) \)

### Step 3: Identify Key Points for \( y = \cos x \)

1. **At \( x = 0 \)**:
\[ y = \cos(0) = 1 \]
2. **At \( x = \frac{\pi}{2} \)**:
\[ y = \cos\left(\frac{\pi}{2}\right) = 0 \]
3. **At \( x = \pi \)**:
\[ y = \cos(\pi) = -1 \]
4. **At \( x = \frac{3\pi}{2} \)**:
\[ y = \cos\left(\frac{3\pi}{2}\right) = 0 \]
5. **At \( x = 2\pi \)**:
\[ y = \cos(2\pi) = 1 \]

### Step 4: Plot the Points for \( y = \cos x \)

- The points to plot are:
- \( (0, 1) \)
- \( \left(\frac{\pi}{2}, 0\right) \)
- \( (\pi, -1) \)
- \( \left(\frac{3\pi}{2}, 0\right) \)
- \( (2\pi, 1) \)

### Step 5: Draw the Graphs

- Connect the points for \( y = \sin x \) with a smooth, wave-like curve that starts at \( (0, 0) \), peaks at \( \left(\frac{\pi}{2}, 1\right) \), returns to \( (\pi, 0) \), dips to \( \left(\frac{3\pi}{2}, -1\right) \), and returns to \( (2\pi, 0) \).

- Connect the points for \( y = \cos x \) with a smooth curve that starts at \( (0, 1) \), drops to \( \left(\frac{\pi}{2}, 0\right) \), reaches \( (\pi, -1) \), returns to \( \left(\frac{3\pi}{2}, 0\right) \), and returns to \( (2\pi, 1) \).

### Step 6: Label the Axes

- Label the x-axis from \( 0 \) to \( 2\pi \) and the y-axis from \( -1 \) to \( 1 \).