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

The value of (cos(pi/3))/(2sin(pi/3)) is (sqrt(3))/6

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(cos(pi/3))/(2sin(pi/3))

\frac{cos ( \frac{π}{3} )}{2 sin ( \frac{π}{3} )}

\frac{3}{6}

Decimal Notation

0.28867 \dots

Solution steps

\frac{cos ( \frac{π}{3} )}{2 sin ( \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}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{\frac{1}{2}}{2 \cdot \frac{3}{2}}

Simplify

\frac{\frac{1}{2}}{2 \cdot \frac{3}{2}} : \frac{3}{6}

\frac{\frac{1}{2}}{2 \cdot \frac{3}{2}}

Apply the fraction rule:

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

= \frac{1}{2 \cdot 2 \cdot \frac{3}{2}}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4 \cdot \frac{3}{2}}

Multiply

4 \cdot \frac{3}{2} : 23

4 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 23

= \frac{1}{2 3}

Rationalize

\frac{1}{2 3} : \frac{3}{6}

\frac{1}{2 3}

Multiply by the conjugate

\frac{3}{3}

= \frac{1 \cdot 3}{2 3 3}

1 \cdot 3 = 3

233 = 6

233

Apply radical rule:

a a = a

33 = 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= \frac{3}{6}

= \frac{3}{6}

= \frac{3}{6}

arcsin (- 9)

13 sin (6 0^{\circ})

cos (\frac{25 π}{3})

tan (arctan (0.2))

4 \cdot cos (\frac{π}{4})

What is the value of (cos(pi/3))/(2sin(pi/3)) ?
The value of (cos(pi/3))/(2sin(pi/3)) is (sqrt(3))/6