Right Triangle X Y Z has a right angle labeled upper Y. The side across from angle upper X is side x, the side across from angle upper Y is side y, and the side across from angle upper Z is side z.

Question

Question
Use the triangle to answer the question.
What is the cosecant of angle X?
(1 point)
Responses

cosecant upper X equals Start Fraction y over z End Fraction
Image with alt text: cosecant upper X equals Start Fraction y over z End Fraction

cosecant upper X equals Start Fraction x over z End Fraction
Image with alt text: cosecant upper X equals Start Fraction x over z End Fraction

cosecant upper X equals Start Fraction y over x End Fraction
Image with alt text: cosecant upper X equals Start Fraction y over x End Fraction

cosecant upper X equals Start Fraction z over x End Fraction

Answer 1

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.