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

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

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cos(arcsin(5/13))

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

\frac{12}{13}

Decimal Notation

0.92307 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

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

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

Simplify

= \frac{12}{13}

arcsec (2)

cos (x) = \frac{2}{2}

- cos (2 π)

arccos (- \frac{1}{2})

cos (x) = - 1

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