What is the value of -sin(2 pi/(12))*2 ?

The value of -sin(2 pi/(12))*2 is -1

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-sin(2 pi/(12))*2

- sin (2 \frac{π}{12}) \cdot 2

- 1

Solution steps

- sin (2 \cdot \frac{π}{12}) \cdot 2

Rewrite using trig identities:

sin (2 \cdot \frac{π}{12}) = \frac{1}{2}

sin (2 \cdot \frac{π}{12})

Simplify:

2 \cdot \frac{π}{12} = \frac{π}{6}

2 \cdot \frac{π}{12}

Multiply fractions:

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

= \frac{π 2}{12}

Cancel the common factor:

2

= \frac{π}{6}

= 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}

= \frac{1}{2}

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

Simplify

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

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

Convert element to fraction:

2 = \frac{2}{1}

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

Cross-cancel:

2

= - 1

= - 1

cos (5 \cdot \frac{π}{2})

sin (4 5^{\circ}) + sin (4 5^{\circ})

arcsin (\frac{1}{1.25})

arctan (sec (0))

sin (- 0.9)