What is the value of sin(arccos(-5/6)) ?

The value of sin(arccos(-5/6)) is (sqrt(11))/6

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sin(arccos(-5/6))

sin (arccos (- \frac{5}{6}))

\frac{11}{6}

Decimal Notation

0.55277 \dots

Solution steps

sin (arccos (- \frac{5}{6}))

Rewrite using trig identities:

sin (arccos (- \frac{5}{6})) = 1 - (- \frac{5}{6})^{2}

Use the following identity:

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

= 1 - (- \frac{5}{6})^{2}

= 1 - (- \frac{5}{6})^{2}

Simplify

= \frac{11}{6}

\frac{tan ( \frac{π}{3} ) + tan ( \frac{π}{4} )}{1 - tan ( \frac{π}{3} ) tan ( \frac{π}{4} )}

cos (9 0^{\circ} + 24 0^{\circ})

cot (\frac{3}{2} π)

cos (3 0^{\circ}) \cdot 10

cot (\frac{15 π}{2})

What is the value of sin(arccos(-5/6)) ?
The value of sin(arccos(-5/6)) is (sqrt(11))/6