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}

\frac{tan ( 2 5 ^{\circ} ) + tan ( 11 0 ^{\circ} )}{1 - tan ( 2 5 ^{\circ} ) tan ( 11 0 ^{\circ} )}

- csc^{2} (\frac{π}{6})

cot (- 18 0^{\circ})

sin (- 5 π)

arccos (- 0.6)

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