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

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

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-cos((2pi)/3)+cos(pi/3)

- cos (\frac{2 π}{3}) + cos (\frac{π}{3})

1

Solution steps

- cos (\frac{2 π}{3}) + cos (\frac{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}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{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}

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

Simplify

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

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

Apply rule

- (- a) = a

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

Add similar elements:

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

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

Multiply fractions:

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

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

Cancel the common factor:

2

= 1

= 1

- 2 sin (2 (\frac{π}{6}))

arctan (\frac{3}{- 3})

cos^{2} (0.18 π)

\frac{1 - cos ( \frac{π}{4} )}{2}

3 sin (π)

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