What is the value of (4sin(60))/(sin(30)) ?

The value of (4sin(60))/(sin(30)) is 4sqrt(3)

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(4sin(60))/(sin(30))

\frac{4 sin ( 6 0 ^{\circ} )}{sin ( 3 0 ^{\circ} )}

43

Decimal Notation

6.92820 \dots

Solution steps

\frac{4 sin ( 6 0 ^{\circ} )}{sin ( 3 0 ^{\circ} )}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

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}

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

Simplify

\frac{4 \cdot \frac{3}{2}}{\frac{1}{2}} : 43

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

Apply the fraction rule:

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

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

Multiply the numbers:

4 \cdot 2 = 8

= \frac{8 \cdot \frac{3}{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 8 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 8}{2}

Divide the numbers:

\frac{8}{2} = 4

= 43

= 43

arccos (\frac{3}{12})

sec (90 0^{\circ})

0 cos (6 0^{\circ})

5 sin (13 5^{\circ})

sin^{2} (3 0^{\circ}) + sec^{2} (4 5^{\circ}) - 6 cos (6 0^{\circ})

What is the value of (4sin(60))/(sin(30)) ?
The value of (4sin(60))/(sin(30)) is 4sqrt(3)