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Popular >

1/3 cos^3(pi)

Solution

\frac{1}{3} cos^{3} (π)

Solution

- \frac{1}{3}

+1

Decimal Notation

- 0.33333 \dots

Solution steps

\frac{1}{3} cos^{3} (π)

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} (- 1)^{3}

Simplify

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

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

(- 1)^{3} = - 1

(- 1)^{3}

Apply exponent rule:

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

if

n

is odd

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

= - 1^{3}

Apply rule

1^{a} = 1

= - 1

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

Remove parentheses:

(- a) = - a

= - \frac{1}{3} \cdot 1

Multiply:

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

= - \frac{1}{3}

= - \frac{1}{3}

Popular Examples

sqrt(2)cos(325)

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sin(arcsin(-3/10))

sin (arcsin (- \frac{3}{10}))

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arccos (- \frac{1}{10})

Frequently Asked Questions (FAQ)

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