2 of 232 of 23 Items

Question

Feature
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
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
Image with alt text: cosecant upper X equals Start Fraction z over x End Fraction
Skip to navigation

Answer 1

To find the cosecant of angle \( X \) in the right triangle, we need to recall the definitions of trigonometric functions.

The cosecant (abbreviated as csc) of an angle is the reciprocal of the sine of that angle.

In a right triangle:

• The sine of angle \( X \) is given by the ratio of the length of the side opposite to angle \( X \) (which is side \( x \)) to the length of the hypotenuse (which is side \( z \)).

Thus, we have: \[ \sin X = \frac{x}{z} \]

Therefore, the cosecant of angle \( X \) is given by: \[ \csc X = \frac{1}{\sin X} = \frac{z}{x} \]

In the given responses, this corresponds to: \[ \text{cosecant } X = \frac{z}{x} \]

So, the correct answer is:

• cosecant upper X equals Start Fraction z over x End Fraction.