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

sin (\frac{3}{5} - \frac{12}{13})

sin (cos (0.1))

cos (\frac{54}{5.93})

csc (- 3.67)

sec^{3} (\frac{π}{2}) - sec (\frac{π}{2}) - sec^{3} (π) - sec (π)

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