Trigonometric function graphs illustrating amplitude, period, and phase shift.

Problem Analysis:

The task involves identifying the correct mathematical expressions for the given waveforms. Each waveform is labeled with a letter (A, B, C, D), and we need to match them with their corresponding mathematical equations from the provided options.

#### Key Concepts:
1. Sine and Cosine Functions:
- Sine and cosine functions are periodic and oscillate between -1 and 1.
- The general form of a sine wave is \( y = A \sin(Bx + C) \), where:
- \( A \) is the amplitude,
- \( B \) affects the period,
- \( C \) is the phase shift.

2. Amplitude:
- The amplitude is the maximum deviation from the centerline (usually the x-axis).

3. Period:
- The period is the length of one complete cycle of the wave.

4. Phase Shift:
- A phase shift occurs when the wave is shifted horizontally along the x-axis.

5. Reflection:
- A negative sign in front of the sine or cosine function reflects the wave across the x-axis.

#### Given Options:
- \( y = \sin(x) \)
- \( y = \cos(x) \)
- \( y = -\sin(x) \)
- \( y = -\cos(x) \)

#### Waveforms:
We need to analyze each waveform (A, B, C, D) and determine which mathematical expression matches it.

---

Step-by-Step Solution:

#### Waveform A:
- Description: This waveform starts at the origin (0, 0) and rises to a positive peak.
- Analysis:
- It resembles a standard sine wave, \( y = \sin(x) \), which starts at 0 and increases.
- There is no reflection or phase shift.
- Match: \( y = \sin(x) \)

#### Waveform B:
- Description: This waveform starts at its maximum value (1) and decreases.
- Analysis:
- It resembles a cosine wave, \( y = \cos(x) \), which starts at 1 and decreases.
- There is no reflection or phase shift.
- Match: \( y = \cos(x) \)

#### Waveform C:
- Description: This waveform starts at the origin (0, 0) but decreases below the x-axis.
- Analysis:
- It resembles a sine wave that is reflected across the x-axis.
- The equation for this is \( y = -\sin(x) \).
- Match: \( y = -\sin(x) \)

#### Waveform D:
- Description: This waveform starts at its minimum value (-1) and increases.
- Analysis:
- It resembles a cosine wave that is reflected across the x-axis.
- The equation for this is \( y = -\cos(x) \).
- Match: \( y = -\cos(x) \)

---

Final Matches:

- A: \( y = \sin(x) \)
- B: \( y = \cos(x) \)
- C: \( y = -\sin(x) \)
- D: \( y = -\cos(x) \)

---

Boxed Answer:

\[
\boxed{A: y = \sin(x), \, B: y = \cos(x), \, C: y = -\sin(x), \, D: y = -\cos(x)}
\]