What is the value of (2sin(30))/(cos(30)) ?

The value of (2sin(30))/(cos(30)) is (2sqrt(3))/3

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(2sin(30))/(cos(30))

\frac{2 sin ( 3 0 ^{\circ} )}{cos ( 3 0 ^{\circ} )}

\frac{2 3}{3}

Decimal Notation

1.15470 \dots

Solution steps

\frac{2 sin ( 3 0 ^{\circ} )}{cos ( 3 0 ^{\circ} )}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

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

Simplify

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

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

Apply the fraction rule:

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

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

Multiply the numbers:

2 \cdot 2 = 4

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

Multiply

4 \cdot \frac{1}{2} : 2

4 \cdot \frac{1}{2}

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= \frac{2}{3}

Rationalize

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

= \frac{2 3}{3}

= \frac{2 3}{3}

tan (\frac{2}{6})

sin (31. 7^{\circ})

cos (\frac{11 π}{20}) cos (\frac{π}{5}) - sin (\frac{11 π}{20}) sin (\frac{π}{5})

\frac{tan ( 5 0 ^{\circ} ) + tan ( 2 0 ^{\circ} )}{1 - tan ( 5 0 ^{\circ} ) tan ( 2 0 ^{\circ} )}

40 \cdot sin (5 3^{\circ})

What is the value of (2sin(30))/(cos(30)) ?
The value of (2sin(30))/(cos(30)) is (2sqrt(3))/3