What is the value of 27sin(30) ?

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27sin(30)

27 sin (3 0^{\circ})

\frac{27}{2}

Decimal Notation

13.5

Solution steps

27 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}

= 27 \cdot \frac{1}{2}

Simplify

27 \cdot \frac{1}{2} : \frac{27}{2}

27 \cdot \frac{1}{2}

Convert element to fraction:

27 = \frac{27}{1}

= \frac{1}{2} \cdot \frac{27}{1}

Multiply fractions:

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

= \frac{27 \cdot 1}{1 \cdot 2}

Cancel the common factor:

1

= \frac{27}{2}

= \frac{27}{2}

\frac{4 sin ( 3 1 ^{\circ} )}{3}

\frac{sec ( 11 π )}{6} \frac{sin ( π )}{6} + \frac{cos ( 7 π )}{6}

sin (2 arctan (\frac{2}{3}))

- arctan (tan (\frac{2 π}{7}))

\frac{40}{cos ( 3 0 ^{\circ} )}