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

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

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

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

- \frac{3 15}{8}

Solution steps

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

= 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}

\frac{tan ( 1 7 ^{\circ} ) + tan ( 1 3 ^{\circ} )}{1 - tan ( 1 7 ^{\circ} ) tan ( 1 3 ^{\circ} )}

arctan (756)

350000 csc (\frac{π}{30} \cdot 5)

cos (arctan (\frac{1}{3}))

cos (arctan (6))

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