What is the value of sin(arccos((sqrt(3))/2)) ?

The value of sin(arccos((sqrt(3))/2)) is 1/2

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sin(arccos((sqrt(3))/2))

sin (arccos (\frac{3}{2}))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

sin (arccos (\frac{3}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{1}{2}

2 cos^{2} (1 5^{\circ}) - 1

2 sin (6 0^{\circ})

arctan (tan (\frac{10 π}{11}))

sin (1 9^{\circ})

cos^{2} (18 0^{\circ})

What is the value of sin(arccos((sqrt(3))/2)) ?
The value of sin(arccos((sqrt(3))/2)) is 1/2