## Trending News

Promoted

# Find the value of sec [Cot^-1 (-6)]?

Find the value of sec [Cot^-1 (-6)]?

### 2 Answers

Relevance

- germanoLv 71 decade agoFavorite Answer
sec [arccot (-6)]

the question is: what is the secant of that arc whose cot is (-6)?

thus let [arccot (-6)] = y

then cot y = - 6

now you have to rewrite sec y in terms of cot y, that is:

sec²y = (1/cos²y) = (cos²y + sin²y)/cos²y =

1 + tan²y = 1 + 1/cot²y = (cot²y + 1)/cot²y

and therefore, being cot y = - 6,

sec y = ±√ [(cot²y + 1)/cot²y] = ± √ {(-6)² + 1]/(-6)²} =

±√ [(36 + 1)/(36)] = ± (√37)/6

as for the sign, being arccot range (0,π), and being cot y negative,

the respective arc belongs to the 2nd quadrant (π/2 < y < π)

and therefore sec y is negative:

in conlcusion,

sec [arccot (-6)] = - (√37)/6

I hope it has been helpful

Bye!

Still have questions? Get your answers by asking now.