What is the value of (cos^3(pi))/3 ?

The value of (cos^3(pi))/3 is -1/3

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(cos^3(pi))/3

\frac{cos ^{3} ( π )}{3}

- \frac{1}{3}

Decimal Notation

- 0.33333 \dots

Solution steps

\frac{cos ^{3} ( π )}{3}

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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}

= (- 1)

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

Simplify

\frac{( - 1 ) ^{3}}{3} : - \frac{1}{3}

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

(- 1)^{3} = - 1

(- 1)^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- 1)^{3} = - 1^{3}

= - 1^{3}

Apply rule

1^{a} = 1

= - 1

= \frac{- 1}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{3}

= - \frac{1}{3}

\frac{tan ( 15 5 ^{\circ} ) - tan ( 3 5 ^{\circ} )}{1 + tan ( 15 5 ^{\circ} ) tan ( 3 5 ^{\circ} )}

arccos (0.62)

arccos (0.54)

arccos (0.79)

arctan (\frac{12}{15})