What is the value of cos(((2pi)/3+2pi)/(4)) ?

The value of cos(((2pi)/3+2pi)/(4)) is -1/2

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cos(((2pi)/3+2pi)/(4))

cos (\frac{\frac{2 π}{3} + 2 π}{4})

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

cos (\frac{\frac{2 π}{3} + 2 π}{4})

Simplify:

\frac{\frac{2 π}{3} + 2 π}{4} = \frac{2 π}{3}

\frac{\frac{2 π}{3} + 2 π}{4}

Join

\frac{2 π}{3} + 2 π : \frac{8 π}{3}

\frac{2 π}{3} + 2 π

Convert element to fraction:

2 π = \frac{2 π 3}{3}

= \frac{2 π}{3} + \frac{2 π 3}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{2 π + 2 π 3}{3}

2 π + 2 π 3 = 8 π

2 π + 2 π 3

Multiply the numbers:

2 \cdot 3 = 6

= 2 π + 6 π

Add similar elements:

2 π + 6 π = 8 π

= 8 π

= \frac{8 π}{3}

= \frac{\frac{8 π}{3}}{4}

Apply the fraction rule:

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

= \frac{8 π}{3 \cdot 4}

Multiply the numbers:

3 \cdot 4 = 12

= \frac{8 π}{12}

Cancel the common factor:

4

= \frac{2 π}{3}

= 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}

= - \frac{1}{2}

tan (arcsin (\frac{20}{29}))

cos (1 0^{\circ}) \cdot 10

csc (\frac{π}{3}) + sin (- 3 0^{\circ})

arctan (- \frac{3}{2}) + π

\frac{1}{cos ^{2} ( \frac{2 π}{3} )}

What is the value of cos(((2pi)/3+2pi)/(4)) ?
The value of cos(((2pi)/3+2pi)/(4)) is -1/2