Question

Find sec x if sin x = -7/25 and cot x = -24/7.
Show work. Thanks.

Answer 1

`sec\ x = (25)/(24)`

Explanation:

Given

`sin\ x = -(7)/(25)`

`cot\ x = -(24)/(7)`

Required

Determine sec x

Sec x is calculated as:

`sec\ x = (1)/(cos\ x)`

Multiply by sin x/sin x

`sec\ x = (1)/(cos\ x) * (sin\ x)/(sin\ x)`

`sec\ x = (1)/(sin\ x) * (sin\ x)/(cos\ x)`

`sec\ x = (1)/(sin\ x) * \tan\ x`

`tan\ x = (1)/(cot\ x)`

`sec\ x = (1)/(sin\ x) * (1)/(cot\ x)`

The equation becomes:

`sec\ x = (1)/(-7/25) * (1)/(-24/7)`

`sec\ x = (-25)/(7) * (-7)/(24)`

`sec\ x = (25)/(24)`