What is the value of -9cos(-pi/6) ?

The value of -9cos(-pi/6) is -(9sqrt(3))/2

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-9cos(-pi/6)

- 9 cos (- \frac{π}{6})

- \frac{9 3}{2}

Decimal Notation

- 7.79422 \dots

Solution steps

- 9 cos (- \frac{π}{6})

Rewrite using trig identities:

cos (- \frac{π}{6}) = \frac{3}{2}

cos (- \frac{π}{6})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{6}) = cos (\frac{π}{6})

= cos (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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{3}{2}

= \frac{3}{2}

= - 9 \cdot \frac{3}{2}

Simplify

- 9 \cdot \frac{3}{2} : - \frac{9 3}{2}

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

Multiply fractions:

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

= - \frac{3 \cdot 9}{2}

= - \frac{9 3}{2}

cos (π) + sin (π) i

tan (\frac{6 π}{6})

csc (5 5^{\circ})

arctan (\frac{tan ( 2 0 ^{\circ} )}{cos ( 1 0 ^{\circ} )})

5 arcsin (1)