What is the value of sin(arccos((sqrt(5))/5)) ?

The value of sin(arccos((sqrt(5))/5)) is (2sqrt(5))/5

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sin(arccos((sqrt(5))/5))

sin (arccos (\frac{5}{5}))

\frac{2 5}{5}

Decimal Notation

0.89442 \dots

Solution steps

sin (arccos (\frac{5}{5}))

Rewrite using trig identities:

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

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

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

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

Simplify

= \frac{2 5}{5}

2 - cos (\frac{π}{2})

- cos (\frac{π}{4}) + 1

tan (\frac{1}{1})

2 sin (\frac{π}{4}) + 2 cos (\frac{π}{4})

arctan (\frac{12}{6})

What is the value of sin(arccos((sqrt(5))/5)) ?
The value of sin(arccos((sqrt(5))/5)) is (2sqrt(5))/5