What is the value of 20cos((2pi)/3) ?

The value of 20cos((2pi)/3) is -10

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20cos((2pi)/3)

20 cos (\frac{2 π}{3})

- 10

Solution steps

20 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}

= 20 (- \frac{1}{2})

Simplify

20 (- \frac{1}{2}) : - 10

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

Remove parentheses:

(- a) = - a

= - 20 \cdot \frac{1}{2}

Multiply fractions:

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

= - \frac{1 \cdot 20}{2}

Multiply the numbers:

1 \cdot 20 = 20

= - \frac{20}{2}

Divide the numbers:

\frac{20}{2} = 10

= - 10

= - 10

\frac{250}{sin ( 4 5 ^{\circ} )}

arctan (\frac{11.2}{18.3})

arctan (\frac{- 1.34}{0.84})

\frac{7}{tan ( 5 0 ^{\circ} )}

cos (7 5^{\circ}) sin (1 5^{\circ}) + sin (7 5^{\circ}) cos (1 5^{\circ})