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

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

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-3sin(pi/3)

- 3 sin (\frac{π}{3})

- \frac{3 3}{2}

Decimal Notation

- 2.59807 \dots

Solution steps

- 3 sin (\frac{π}{3})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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{3}{2}

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

Simplify

- 3 \cdot \frac{3}{2} : - \frac{3 3}{2}

- 3 \cdot \frac{3}{2}

Multiply fractions:

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

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

= - \frac{3 3}{2}

cos^{2} (4 5^{\circ}) - sin^{2} (4 5^{\circ})

- cos^{2} (0)

5 cos (π)

tan (- \frac{3}{3})

cos (\frac{6 π}{3})