What is the value of sec(arcsin(5/13)) ?

The value of sec(arcsin(5/13)) is 13/12

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sec(arcsin(5/13))

sec (arcsin (\frac{5}{13}))

\frac{13}{12}

Decimal Notation

1.08333 \dots

Solution steps

sec (arcsin (\frac{5}{13}))

Rewrite using trig identities:

sec (arcsin (\frac{5}{13})) = \frac{1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

Use the following identity:

sec (arcsin (x)) = \frac{1 - x ^{2}}{1 - x ^{2}}

= \frac{1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

= \frac{1 - ( \frac{5}{13} ) ^{2}}{1 - ( \frac{5}{13} ) ^{2}}

Simplify

= \frac{13}{12}

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

sin^{2} (\frac{π}{12})

\frac{cos ( 1 )}{1}

cos (arcsin (\frac{2}{3}))

arctan (\frac{1}{12})

What is the value of sec(arcsin(5/13)) ?
The value of sec(arcsin(5/13)) is 13/12