In a right triangle, the cosecant of an angle is defined as the ratio of the length of the hypotenuse to the length of the side opposite the angle.
Given the triangle X Y Z with:
- \( Y \) as the right angle
- Side opposite angle \( X \) is \( x \)
- Side opposite angle \( Y \) (the right angle) is \( y \)
- Side opposite angle \( Z \) is \( z \) (hypotenuse)
To find the cosecant of angle \( X \), we use the definition:
\[ \text{cosecant } X = \frac{\text{hypotenuse}}{\text{side opposite angle } X} = \frac{z}{x} \]
Therefore, the correct response is:
cosecant upper X equals Start Fraction z over x End Fraction.