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Popular >

cos^4(pi/3)

Solution

cos^{4} (\frac{π}{3})

Solution

\frac{1}{16}

+1

Decimal Notation

0.0625

Solution steps

cos^{4} (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

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

Simplify

(\frac{1}{2})^{4} : \frac{1}{16}

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

Apply exponent rule:

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

= \frac{1 ^{4}}{2 ^{4}}

Apply rule

1^{a} = 1

1^{4} = 1

= \frac{1}{2 ^{4}}

2^{4} = 16

= \frac{1}{16}

= \frac{1}{16}

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Frequently Asked Questions (FAQ)

What is the value of cos^4(pi/3) ?
The value of cos^4(pi/3) is 1/16