For $s = \pi$, we want to determine the point on the unit circle, as well as $\cos(\pi)$ and $\sin(\pi)$, and state which trigonometric functions are not defined.

Unit Circle Position:

• The angle $s = \pi$ corresponds to 180 degrees or a half turn around the unit circle.
• The point on the unit circle for $s = \pi$ is $(-1, 0)$.

$\cos(\pi)$ and $\sin(\pi)$:

• $\cos(\pi) = -1$, since cosine corresponds to the x-coordinate of the point on the unit circle.
• $\sin(\pi) = 0$, since sine corresponds to the y-coordinate of the point on the unit circle.

Undefined Functions:

• The tangent function, $\tan(s)$, is defined as $\frac{\sin(s)}{\cos(s)}$. Since $\cos(\pi) = -1$ and $\sin(\pi) = 0$, $\tan(\pi) = 0$ and is defined.
• The cotangent function, $\cot(s) = \frac{1}{\tan(s)}$, is undefined at $s = \pi$ because $\tan(\pi) = 0$, and division by zero is undefined.
• The secant function, $\sec(s) = \frac{1}{\cos(s)}$, is defined as $\sec(\pi) = \frac{1}{-1} = -1$.
• The cosecant function, $\csc(s) = \frac{1}{\sin(s)}$, is undefined because $\sin(\pi) = 0$.

Summary:

• $\cos(\pi) = -1$
• $\sin(\pi) = 0$
• Functions not defined at $\pi$: $\csc(\pi)$ and $\cot(\pi)$

Would you like more details or have any questions?

Here are five related questions to explore:

1. What are the values of cosine and sine at $s = 2\pi$?
2. How do you calculate tangent and secant for angles on the unit circle?
3. What is the geometric interpretation of the unit circle?
4. What are the values of trigonometric functions for $s = \frac{\pi}{2}$?
5. What happens to trigonometric functions for angles greater than $2\pi$?

Tip: When dealing with trigonometric functions, remember that their signs depend on the quadrant in which the angle lies.