Answer:
[tex]sec\ x = \frac{25}{24}[/tex]
Step-by-step explanation:
Given
[tex]sin\ x = -\frac{7}{25}[/tex]
[tex]cot\ x = -\frac{24}{7}[/tex]
Required
Determine sec x
Sec x is calculated as:
[tex]sec\ x = \frac{1}{cos\ x}[/tex]
Multiply by sin x/sin x
[tex]sec\ x = \frac{1}{cos\ x} * \frac{sin\ x}{sin\ x}[/tex]
[tex]sec\ x = \frac{1}{sin\ x} * \frac{sin\ x}{cos\ x}[/tex]
[tex]sec\ x = \frac{1}{sin\ x} * \tan\ x[/tex]
[tex]tan\ x = \frac{1}{cot\ x}[/tex]
[tex]sec\ x = \frac{1}{sin\ x} * \frac{1}{cot\ x}[/tex]
The equation becomes:
[tex]sec\ x = \frac{1}{-7/25} * \frac{1}{-24/7}[/tex]
[tex]sec\ x = \frac{-25}{7} * \frac{-7}{24}[/tex]
[tex]sec\ x = \frac{25}{24}[/tex]
