find the exact value of each of the remaining trigonometric functions of 0. cos0 =0 -7/2

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!

Discover the exact values of the six trigonometric functions at 0 degrees (0 radians), including sin(0), cos(0), tan(0), cot(0), sec(0), and csc(0). Learn the key trigonometric relationships and formulas based on the unit circle. This problem is suitable for students in Grades 9-11.

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