What is the value of sin(arccos(-1/5)) ?

The value of sin(arccos(-1/5)) is (2sqrt(6))/5

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sin(arccos(-1/5))

sin (arccos (- \frac{1}{5}))

\frac{2 6}{5}

Decimal

0.97979 \dots

Solution steps

sin (arccos (- \frac{1}{5}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{2 6}{5}

sin (arctan (\frac{2}{5}))

\frac{sin ( 6 0 ^{\circ} ) \cdot tan ( 3 0 ^{\circ} )}{sec ( 4 5 ^{\circ} )}

- 4 π^{2} cos (π + \frac{π}{4})

sin (\frac{13}{12} π)

22 cos (4 5^{\circ})

What is the value of sin(arccos(-1/5)) ?
The value of sin(arccos(-1/5)) is (2sqrt(6))/5