What is the value of (1166.67)/(sin(45)) ?

The value of (1166.67)/(sin(45)) is (116667sqrt(2))/(100)

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(1166.67)/(sin(45))

\frac{1166.67}{sin ( 4 5 ^{\circ} )}

\frac{116667 2}{100}

Decimal Notation

1649.92053 \dots

Solution steps

\frac{1166.67}{sin ( 4 5 ^{\circ} )}

= \frac{\frac{116667}{100}}{sin ( 4 5 ^{\circ} )}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

= \frac{\frac{116667}{100}}{\frac{2}{2}}

Simplify

\frac{\frac{116667}{100}}{\frac{2}{2}} : \frac{116667 2}{100}

\frac{\frac{116667}{100}}{\frac{2}{2}}

Divide fractions:

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

= \frac{116667 \cdot 2}{100 2}

Multiply the numbers:

116667 \cdot 2 = 233334

= \frac{233334}{100 2}

Cancel the common factor:

2

= \frac{116667}{50 2}

Rationalize

\frac{116667}{50 2} : \frac{116667 2}{100}

\frac{116667}{50 2}

Multiply by the conjugate

\frac{2}{2}

= \frac{116667 2}{50 2 2}

5022 = 100

5022

Apply radical rule:

a a = a

22 = 2

= 50 \cdot 2

Multiply the numbers:

50 \cdot 2 = 100

= 100

= \frac{116667 2}{100}

= \frac{116667 2}{100}

= \frac{116667 2}{100}

4 sin (0) - sin (0)

- cos (\frac{2 π}{3}) - (- cos (\frac{π}{3}))

sin (\frac{3}{5} - \frac{12}{13})

sin (cos (0.1))

cos (\frac{54}{5.93})

What is the value of (1166.67)/(sin(45)) ?
The value of (1166.67)/(sin(45)) is (116667sqrt(2))/(100)