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

The value of sin(arccos((sqrt(2))/2)) is sqrt(1/2)

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sin(arccos((sqrt(2))/2))

sin (arccos (\frac{2}{2}))

\frac{1}{2}

Decimal Notation

0.70710 \dots

Solution steps

sin (arccos (\frac{2}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{1}{2}

arccos (2)

sin (5 3^{\circ})

sin (5 5^{\circ})

tan (2 0^{\circ})

arccot (- \frac{3}{3})

What is the value of sin(arccos((sqrt(2))/2)) ?
The value of sin(arccos((sqrt(2))/2)) is sqrt(1/2)