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

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20cos(pi/3)

20 cos (\frac{π}{3})

10

Solution steps

20 cos (\frac{π}{3})

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}

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

Simplify

20 \cdot \frac{1}{2} : 10

20 \cdot \frac{1}{2}

Convert element to fraction:

20 = \frac{20}{1}

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

Cross-cancel common factor:

2

= \frac{10}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 10

= 10

4 arctan (\frac{1}{5}) - arctan (\frac{1}{239})

csc (\frac{6 π}{5})

\frac{4}{tan ( 4 5 ^{\circ} )}

50 sin^{3} (\frac{π}{3})

cos^{4} (3 0^{\circ})