Which of the following trigonometric ratios has a value that is undefined?

Question

(1 point)
Responses

csc π
csc π

sec π
sec π

sin π
sin π

tan π

Answer 1

To determine which of the given trigonometric ratios has a value that is undefined, we can evaluate each ratio:

1. csc π: The cosecant function is defined as \( csc(x) = \frac{1}{sin(x)} \). Since \( sin(π) = 0 \), \( csc(π) = \frac{1}{0} \) is undefined.

2. sec π: The secant function is defined as \( sec(x) = \frac{1}{cos(x)} \). Since \( cos(π) = -1 \), \( sec(π) = \frac{1}{-1} = -1 \), which is defined.

3. sin π: \( sin(π) = 0 \), which is defined.

4. tan π: The tangent function is defined as \( tan(x) = \frac{sin(x)}{cos(x)} \). Since \( sin(π) = 0 \) and \( cos(π) = -1 \), \( tan(π) = \frac{0}{-1} = 0 \), which is defined.

Thus, the only trigonometric ratio from the list that is undefined is:

csc π.