What is the value of sec(arctan(6)) ?

The value of sec(arctan(6)) is square root of 37

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sec(arctan(6))

sec (arctan (6))

37

Decimal Notation

6.08276 \dots

Solution steps

sec (arctan (6))

Rewrite using trig identities:

sec (arctan (6)) = 1 + 6^{2}

Use the following identity:

sec (arctan (x)) = 1 + x^{2}

= 1 + 6^{2}

= 1 + 6^{2}

Simplify

= 37

120 cos (6 0^{\circ})

csc (\frac{- π}{3})

120 sin (3 0^{\circ})

csc (\frac{- π}{2})

sin (arcsin (\frac{8}{17}) + arccos (- \frac{3}{5}))

What is the value of sec(arctan(6)) ?
The value of sec(arctan(6)) is square root of 37