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Find sec x if sin x = -7/25 and cot x = -24/7.
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User Igor S
by
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1 Answer

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Answer:


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)

User Matthias Robbers
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