What is the value of (-313.3)/(sin(60)) ?

The value of (-313.3)/(sin(60)) is -(3133sqrt(3))/(15)

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(-313.3)/(sin(60))

\frac{- 313.3}{sin ( 6 0 ^{\circ} )}

- \frac{3133 3}{15}

Decimal Notation

- 361.76767 \dots

Solution steps

\frac{- 313.3}{sin ( 6 0 ^{\circ} )}

= \frac{- \frac{3133}{10}}{sin ( 6 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}

= \frac{- \frac{3133}{10}}{\frac{3}{2}}

Simplify

\frac{- \frac{3133}{10}}{\frac{3}{2}} : - \frac{3133 3}{15}

\frac{- \frac{3133}{10}}{\frac{3}{2}}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{3133}{10}}{\frac{3}{2}}

Divide fractions:

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

= - \frac{3133 \cdot 2}{10 3}

Multiply the numbers:

3133 \cdot 2 = 6266

= - \frac{6266}{10 3}

Cancel the common factor:

2

= - \frac{3133}{5 3}

Rationalize

- \frac{3133}{5 3} : - \frac{3133 3}{15}

- \frac{3133}{5 3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{3133 3}{5 3 3}

533 = 15

533

Apply radical rule:

a a = a

33 = 3

= 5 \cdot 3

Multiply the numbers:

5 \cdot 3 = 15

= 15

= - \frac{3133 3}{15}

= - \frac{3133 3}{15}

= - \frac{3133 3}{15}

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

\frac{1 + sin ( \frac{π}{2} )}{1 - cos ( 2 π )}

8 sin (1 5^{\circ})

sin (30 5^{\circ})

sin (2 5^{\circ}) \cdot 20

What is the value of (-313.3)/(sin(60)) ?
The value of (-313.3)/(sin(60)) is -(3133sqrt(3))/(15)