What is the value of -2cos(3*pi/6) ?

The value of -2cos(3*pi/6) is 0

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-2cos(3*pi/6)

- 2 cos (3 \cdot \frac{π}{6})

0

Solution steps

- 2 cos (3 \cdot \frac{π}{6})

Rewrite using trig identities:

cos (3 \cdot \frac{π}{6}) = 0

cos (3 \cdot \frac{π}{6})

Simplify:

3 \cdot \frac{π}{6} = \frac{π}{2}

3 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 3}{6}

Cancel the common factor:

3

= \frac{π}{2}

= cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0

= - 2 \cdot 0

Simplify

= 0

sech (ln (10))

cos (2 π \cdot 2)

arctan (\frac{20}{12})

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

5 sin (1 0^{\circ})