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

The value of cos(4(-pi/6)) is -1/2

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cos(4(-pi/6))

cos (4 (- \frac{π}{6}))

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

cos (4 (- \frac{π}{6}))

Simplify:

4 (- \frac{π}{6}) = - \frac{2 π}{3}

4 (- \frac{π}{6})

Remove parentheses:

(- a) = - a

= - 4 \cdot \frac{π}{6}

Multiply fractions:

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

= - \frac{π 4}{6}

Cancel the common factor:

2

= - \frac{2 π}{3}

= cos (- \frac{2 π}{3})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{2 π}{3}) = cos (\frac{2 π}{3})

= cos (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 π}{3})

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}

= - \frac{1}{2}

= - \frac{1}{2}

cot (\frac{- 7 π}{6})

40 sin (5 0^{\circ})

sin (\frac{2}{3}) π

1.5 \cdot sin (4 5^{\circ})

4 tan (\frac{π}{6}) + 2 cot (\frac{π}{3})