What is the value of sec(arctan(2/3)) ?

The value of sec(arctan(2/3)) is (sqrt(13))/3

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sec(arctan(2/3))

sec (arctan (\frac{2}{3}))

\frac{13}{3}

Decimal Notation

1.20185 \dots

Solution steps

sec (arctan (\frac{2}{3}))

Rewrite using trig identities:

sec (arctan (\frac{2}{3})) = 1 + (\frac{2}{3})^{2}

Use the following identity:

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

= 1 + (\frac{2}{3})^{2}

= 1 + (\frac{2}{3})^{2}

Simplify

= \frac{13}{3}

2 sec^{2} (\frac{π}{6}) tan (\frac{π}{6})

csc (\frac{7 π}{12})

2 cos (- π)

\frac{cos ( 3 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

arctan (\frac{- 8}{6})

What is the value of sec(arctan(2/3)) ?
The value of sec(arctan(2/3)) is (sqrt(13))/3