What is the value of -cos(0)+(cos^3(0))/3 ?

The value of -cos(0)+(cos^3(0))/3 is -2/3

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-cos(0)+(cos^3(0))/3

- cos (0) + \frac{cos ^{3} ( 0 )}{3}

- \frac{2}{3}

Decimal Notation

- 0.66666 \dots

Solution steps

- cos (0) + \frac{cos ^{3} ( 0 )}{3}

Use the following trivial identity:

cos (0) = 1

cos (0)

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

= - 1 + \frac{1 ^{3}}{3}

Simplify

- 1 + \frac{1 ^{3}}{3} : - \frac{2}{3}

- 1 + \frac{1 ^{3}}{3}

Apply rule

1^{a} = 1

1^{3} = 1

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

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

- 1 \cdot 3 + 1 = - 2

- 1 \cdot 3 + 1

Multiply the numbers:

1 \cdot 3 = 3

= - 3 + 1

Add/Subtract the numbers:

- 3 + 1 = - 2

= - 2

= \frac{- 2}{3}

Apply the fraction rule:

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

= - \frac{2}{3}

= - \frac{2}{3}

\frac{5}{sin ( 5 0 ^{\circ} )}

arcsin (\frac{- π}{6})

\frac{600}{370} cos (6 6^{\circ})

\frac{7}{cos ( 7 1 ^{\circ} )}

arccos (\frac{2}{6})

What is the value of -cos(0)+(cos^3(0))/3 ?
The value of -cos(0)+(cos^3(0))/3 is -2/3