What is the value of sin((-3pi)/4) ?

The value of sin((-3pi)/4) is -(sqrt(2))/2

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sin((-3pi)/4)

sin (\frac{- 3 π}{4})

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

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}

cos (12 5^{\circ})

arccos (\frac{1}{5})

sin (- \frac{5 π}{8})

8 sin (3 0^{\circ})

sin (- 27 0^{\circ})