What is the value of cos(arcsin(2/3)) ?

The value of cos(arcsin(2/3)) is (sqrt(5))/3

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cos(arcsin(2/3))

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

\frac{5}{3}

Decimal Notation

0.74535 \dots

Solution steps

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

Rewrite using trig identities:

cos (arcsin (\frac{2}{3})) = 1 - (\frac{2}{3})^{2}

Use the following identity:

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

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

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

Simplify

= \frac{5}{3}

arctan (\frac{1}{12})

arctan (\frac{2}{1.5})

8 sin (4 5^{\circ})

sin (\frac{29 π}{6})

cos^{4} (π)

What is the value of cos(arcsin(2/3)) ?
The value of cos(arcsin(2/3)) is (sqrt(5))/3