What is the value of (0.4)/(sin(30)) ?

The value of (0.4)/(sin(30)) is 4/5

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(0.4)/(sin(30))

\frac{0.4}{sin ( 3 0 ^{\circ} )}

\frac{4}{5}

Decimal Notation

0.8

Solution steps

\frac{0.4}{sin ( 3 0 ^{\circ} )}

= \frac{\frac{2}{5}}{sin ( 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}

= \frac{\frac{2}{5}}{\frac{1}{2}}

Simplify

\frac{\frac{2}{5}}{\frac{1}{2}} : \frac{4}{5}

\frac{\frac{2}{5}}{\frac{1}{2}}

Divide fractions:

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

= \frac{2 \cdot 2}{5 \cdot 1}

Refine

= \frac{2 \cdot 2}{5}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4}{5}

= \frac{4}{5}

\frac{100}{cos ( 6 0 ^{\circ} )}

\frac{50}{sin ( 6 0 ^{\circ} )}

sec^{2} (\frac{11 π}{6})

cot (- 84 0^{\circ})

42 tan (3 8^{\circ})