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Popular >

sin^3(pi/6)

Solution

sin^{3} (\frac{π}{6})

Solution

\frac{1}{8}

+1

Decimal Notation

0.125

Solution steps

sin^{3} (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= (\frac{1}{2})^{3}

Simplify

(\frac{1}{2})^{3} : \frac{1}{8}

(\frac{1}{2})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{3}}{2 ^{3}}

Apply rule

1^{a} = 1

1^{3} = 1

= \frac{1}{2 ^{3}}

2^{3} = 8

= \frac{1}{8}

= \frac{1}{8}

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1 - cos^{2} (0)

tan (- \frac{9 π}{4})

tan (6 9^{\circ})

tan (\frac{31 π}{6})

Frequently Asked Questions (FAQ)

What is the value of sin^3(pi/6) ?
The value of sin^3(pi/6) is 1/8