What is the value of sec(arcsin(24/25)) ?

The value of sec(arcsin(24/25)) is 25/7

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sec(arcsin(24/25))

sec (arcsin (\frac{24}{25}))

\frac{25}{7}

Decimal Notation

3.57142 \dots

Solution steps

sec (arcsin (\frac{24}{25}))

Rewrite using trig identities:

sec (arcsin (\frac{24}{25})) = \frac{1 - ( \frac{24}{25} ) ^{2}}{1 - ( \frac{24}{25} ) ^{2}}

Use the following identity:

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

= \frac{1 - ( \frac{24}{25} ) ^{2}}{1 - ( \frac{24}{25} ) ^{2}}

= \frac{1 - ( \frac{24}{25} ) ^{2}}{1 - ( \frac{24}{25} ) ^{2}}

Simplify

= \frac{25}{7}

400 sin (6 0^{\circ})

sin^{2} (6 0^{\circ}) + cos^{2} (6 0^{\circ})

arcsin (\frac{2.5}{5})

5 cos (5 0^{\circ})

cos (\frac{5}{2} π)

What is the value of sec(arcsin(24/25)) ?
The value of sec(arcsin(24/25)) is 25/7