What is the value of (2.5)/(sin(30)) ?

The value of (2.5)/(sin(30)) is 5

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(2.5)/(sin(30))

\frac{2.5}{sin ( 3 0 ^{\circ} )}

5

Solution steps

\frac{2.5}{sin ( 3 0 ^{\circ} )}

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

Simplify

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

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

Divide fractions:

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

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

Refine

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

Cancel the common factor:

2

= 5

= 5

arctan (- \frac{6}{6})

sin (arcsin (\frac{9}{41}) + arccos (- \frac{5}{13}))

sin (- 31 5^{\circ}) sin (- 1 5^{\circ})

csc (- \frac{13 π}{6})

tan (12. 5^{\circ})