What is the value of 2sin(3arccos(-1/4)) ?

The value of 2sin(3arccos(-1/4)) is -(3sqrt(15))/8

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2sin(3arccos(-1/4))

2 sin (3 arccos (- \frac{1}{4}))

- \frac{3 15}{8}

Solution steps

2 sin (3 arccos (- \frac{1}{4}))

Rewrite using trig identities:

sin (3 arccos (- \frac{1}{4})) = 3 sin (arccos (- \frac{1}{4})) - 4 sin^{3} (arccos (- \frac{1}{4}))

= 2 (3 sin (arccos (- \frac{1}{4})) - 4 sin^{3} (arccos (- \frac{1}{4})))

Rewrite using trig identities:

sin (arccos (- \frac{1}{4})) = \frac{15}{4}

= 2 3 \cdot \frac{15}{4} - 4 (\frac{15}{4})^{3}

Simplify

2 3 \cdot \frac{15}{4} - 4 (\frac{15}{4})^{3} : - \frac{3 15}{8}

= - \frac{3 15}{8}

arcsin (1.15)

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

csch (1)

cos (π) + i

4 arcsin (1)

What is the value of 2sin(3arccos(-1/4)) ?
The value of 2sin(3arccos(-1/4)) is -(3sqrt(15))/8