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

The value of sec(arctan((3sqrt(2))/2)) is sqrt(11/2)

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sec(arctan((3sqrt(2))/2))

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

\frac{11}{2}

Decimal Notation

2.34520 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{11}{2}

\frac{10 0 ^{2} ( 2 sin ( 3 0 ^{\circ} ) )}{9.8} - 999.984741

\frac{sin ( 8 0 ^{\circ} ) + sin ( 2 0 ^{\circ} )}{cos ( 8 0 ^{\circ} ) + cos ( 2 0 ^{\circ} )}

8 cos (\frac{π}{2} + 0.1)

ln (2 + tan (\frac{3 π}{32}))

sin (\frac{1}{( \frac{2}{9 π} )})

What is the value of sec(arctan((3sqrt(2))/2)) ?
The value of sec(arctan((3sqrt(2))/2)) is sqrt(11/2)