What is the value of sin(arccos(-1/4)) ?

The value of sin(arccos(-1/4)) is (sqrt(15))/4

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sin(arccos(-1/4))

sin (arccos (- \frac{1}{4}))

\frac{15}{4}

Decimal Notation

0.96824 \dots

Solution steps

sin (arccos (- \frac{1}{4}))

Rewrite using trig identities:

sin (arccos (- \frac{1}{4})) = 1 - (- \frac{1}{4})^{2}

Use the following identity:

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

= 1 - (- \frac{1}{4})^{2}

= 1 - (- \frac{1}{4})^{2}

Simplify

= \frac{15}{4}

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What is the value of sin(arccos(-1/4)) ?
The value of sin(arccos(-1/4)) is (sqrt(15))/4