What is the value of -6sin((3pi)/4) ?

The value of -6sin((3pi)/4) is -3sqrt(2)

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-6sin((3pi)/4)

- 6 sin (\frac{3 π}{4})

- 32

Decimal Notation

- 4.24264 \dots

Solution steps

- 6 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}

= - 6 \cdot \frac{2}{2}

Simplify

- 6 \cdot \frac{2}{2} : - 32

- 6 \cdot \frac{2}{2}

Multiply fractions:

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

= - \frac{2 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= - 32

= - 32

sec^{2} (\frac{π}{3}) \cdot (- 0.1)

200 \cdot cos (3 0^{\circ})

arctan (tan (π))

tan (- 0.5)

sec (\frac{15 π}{4})