It seems like there's a misunderstanding in your input. You mentioned that $\cos(0) = -\frac{7}{2}$, but the cosine of $0$ is actually $1$, not $-\frac{7}{2}$. Let's first clarify the correct trigonometric values for $0$.

The exact values of the trigonometric functions at $0$ radians are:

• $\sin(0) = 0$
• $\cos(0) = 1$
• $\tan(0) = 0$
• $\cot(0) = \text{undefined}$ (since $\tan(0) = 0$, and $\cot(\theta) = \frac{1}{\tan(\theta)}$)
• $\sec(0) = 1$ (since $\sec(\theta) = \frac{1}{\cos(\theta)}$)
• $\csc(0) = \text{undefined}$ (since $\csc(\theta) = \frac{1}{\sin(\theta)}$)

Would you like further clarification, or is there any specific part you'd like more details on?

Here are 5 follow-up questions to deepen your understanding:

1. What is the geometric interpretation of the unit circle for $\theta = 0$?
2. How are the undefined trigonometric functions (like $\cot(0)$ and $\csc(0)$) determined?
3. Can you explain why $\tan(0) = 0$?
4. What happens to trigonometric functions as $\theta$ approaches $0$ from positive and negative directions?
5. What is the relationship between the six trigonometric functions at key angles (e.g., $0^\circ$, $90^\circ$, $180^\circ$, etc.)?

Tip: Memorizing trigonometric function values at special angles (like $0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$, and $90^\circ$) helps in solving many trigonometric problems quickly!