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

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-4sin(pi/6)

- 4 sin (\frac{π}{6})

- 2

Solution steps

- 4 sin (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

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{1}{2}

= - 4 \cdot \frac{1}{2}

Simplify

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

- 4 \cdot \frac{1}{2}

Convert element to fraction:

4 = \frac{4}{1}

= \frac{4}{1} \cdot \frac{1}{2}

Cross-cancel common factor:

2

= - \frac{2}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{2}{1} = 2

= - 2

= - 2

- \frac{1}{2} cos (2 π)

sin (- 17 π)

arctan (\frac{1.3}{2.5})

3 \cdot sin (2 0^{\circ})

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