What is the value of | 1/(sin(\frac{-3pi){4})}| ?

The value of | 1/(sin(\frac{-3pi){4})}| is square root of 2

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| 1/(sin(\frac{-3pi){4})}|

\frac{1}{sin ( \frac{- 3 π}{4} )}

2

Decimal Notation

1.41421 \dots

Solution steps

\frac{1}{sin ( \frac{- 3 π}{4} )}

Rewrite using trig identities:

sin (\frac{- 3 π}{4}) = - \frac{2}{2}

sin (\frac{- 3 π}{4})

Simplify

= sin (- \frac{3 π}{4})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{3 π}{4}) = - sin (\frac{3 π}{4})

= - sin (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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{2}{2}

= \frac{1}{- \frac{2}{2}}

Simplify

\frac{1}{- \frac{2}{2}} : 2

\frac{1}{- \frac{2}{2}}

Simplify

\frac{1}{- \frac{2}{2}} : - \frac{2}{2}

\frac{1}{- \frac{2}{2}}

Apply the fraction rule:

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

= - \frac{1}{\frac{2}{2}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

= - \frac{2}{2}

= - \frac{2}{2}

Cancel

\frac{2}{2} : 2

\frac{2}{2}

Cancel

\frac{2}{2} : 2

\frac{2}{2}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{2}{2 ^{\frac{1}{2}}}

Apply exponent rule:

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

\frac{2 ^{1}}{2 ^{\frac{1}{2}}} = 2^{1 - \frac{1}{2}}

= 2^{1 - \frac{1}{2}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= 2^{\frac{1}{2}}

Apply radical rule:

2^{\frac{1}{2}} = 2

= 2

= 2

= - 2

Apply absolute rule:

∣ - a ∣ = a

= 2

= 2

tan (\frac{11}{60})

\frac{π}{2} cos (π)

e - 4 π + sin (1)

csc^{2} (9 0^{\circ})

arcsin (0.904)

What is the value of | 1/(sin(\frac{-3pi){4})}| ?
The value of | 1/(sin(\frac{-3pi){4})}| is square root of 2