What is the value of cos(arcsin(5/8)) ?

The value of cos(arcsin(5/8)) is (sqrt(39))/8

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cos(arcsin(5/8))

cos (arcsin (\frac{5}{8}))

\frac{39}{8}

Decimal Notation

0.78062 \dots

Solution steps

cos (arcsin (\frac{5}{8}))

Rewrite using trig identities:

cos (arcsin (\frac{5}{8})) = 1 - (\frac{5}{8})^{2}

Use the following identity:

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

= 1 - (\frac{5}{8})^{2}

= 1 - (\frac{5}{8})^{2}

Simplify

= \frac{39}{8}

- \frac{1}{6} cos^{3} (0)

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What is the value of cos(arcsin(5/8)) ?
The value of cos(arcsin(5/8)) is (sqrt(39))/8