What is the value of cos^6(pi/4) ?

The value of cos^6(pi/4) is 1/8

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cos^6(pi/4)

cos^{6} (\frac{π}{4})

\frac{1}{8}

Decimal Notation

0.125

Solution steps

cos^{6} (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

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{2}{2}

= (\frac{2}{2})^{6}

Simplify

(\frac{2}{2})^{6} : \frac{1}{8}

(\frac{2}{2})^{6}

Apply exponent rule:

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

= \frac{( 2 ) ^{6}}{2 ^{6}}

(2)^{6} : 2^{3}

Apply radical rule:

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

= (2^{\frac{1}{2}})^{6}

Apply exponent rule:

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

= 2^{\frac{1}{2} \cdot 6}

\frac{1}{2} \cdot 6 = 3

\frac{1}{2} \cdot 6

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 6}{2}

Multiply the numbers:

1 \cdot 6 = 6

= \frac{6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 3

= 2^{3}

= \frac{2 ^{3}}{2 ^{6}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{3}}{2 ^{6}} = \frac{1}{2 ^{6 - 3}}

= \frac{1}{2 ^{6 - 3}}

Subtract the numbers:

6 - 3 = 3

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

2^{3} = 8

= \frac{1}{8}

= \frac{1}{8}

cos (10 9^{\circ})

\frac{arctan ( 2 π )}{2}

3 \cdot sin (0)

sec^{2} (- \frac{π}{2})

2 + 4 sin (1 5^{\circ})