What is the value of 1-cos((2pi)/3) ?

The value of 1-cos((2pi)/3) is 3/2

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1-cos((2pi)/3)

1 - cos (\frac{2 π}{3})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

1 - cos (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 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}

= 1 - (- \frac{1}{2})

Simplify

1 - (- \frac{1}{2}) : \frac{3}{2}

1 - (- \frac{1}{2})

Apply rule

- (- a) = a

= 1 + \frac{1}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 2 + 1 = 3

1 \cdot 2 + 1

Multiply the numbers:

1 \cdot 2 = 2

= 2 + 1

Add the numbers:

2 + 1 = 3

= 3

= \frac{3}{2}

= \frac{3}{2}

- π^{2} cos (2 π)

\frac{1}{sin ( 2 0 ^{\circ} )}

arctan (\frac{1.79}{9.8} + 0.6)

4 cos (18 0^{\circ})

cot^{2} (4 5^{\circ})