What is the value of cos(arcsin((sqrt(45))/7)) ?

The value of cos(arcsin((sqrt(45))/7)) is 2/7

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cos(arcsin((sqrt(45))/7))

cos (arcsin (\frac{45}{7}))

\frac{2}{7}

Decimal

0.28571 \dots

Solution steps

cos (arcsin (\frac{45}{7}))

Rewrite using trig identities:

cos (arcsin (\frac{45}{7})) = 1 - (\frac{45}{7})^{2}

Use the following identity:

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

= 1 - (\frac{45}{7})^{2}

= 1 - (\frac{45}{7})^{2}

Simplify

= \frac{2}{7}

What is the value of cos(arcsin((sqrt(45))/7)) ?
The value of cos(arcsin((sqrt(45))/7)) is 2/7