What is the value of sec(arctan(8/9)) ?

The value of sec(arctan(8/9)) is (sqrt(145))/9

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sec(arctan(8/9))

sec (arctan (\frac{8}{9}))

\frac{145}{9}

Decimal Notation

1.33795 \dots

Solution steps

sec (arctan (\frac{8}{9}))

Rewrite using trig identities:

sec (arctan (\frac{8}{9})) = 1 + (\frac{8}{9})^{2}

Use the following identity:

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

= 1 + (\frac{8}{9})^{2}

= 1 + (\frac{8}{9})^{2}

Simplify

= \frac{145}{9}

cos (2 π) + sin (2 π)

400 \cdot cos (3 0^{\circ})

arctan (16)

cos (\frac{9 π}{10})

cos (\frac{10 π}{4})

What is the value of sec(arctan(8/9)) ?
The value of sec(arctan(8/9)) is (sqrt(145))/9