What is the value of -7cos(-pi/6) ?

The value of -7cos(-pi/6) is -(7sqrt(3))/2

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-7cos(-pi/6)

- 7 cos (- \frac{π}{6})

- \frac{7 3}{2}

Decimal Notation

- 6.06217 \dots

Solution steps

- 7 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}

= - 7 \cdot \frac{3}{2}

Simplify

- 7 \cdot \frac{3}{2} : - \frac{7 3}{2}

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

Multiply fractions:

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

= - \frac{3 \cdot 7}{2}

= - \frac{7 3}{2}

sin (2.7)

sin (4 5^{\circ}) \cdot 2

sec (arccos (- \frac{3}{4}))

cos (3 π) + sin (3 π)

arctan (\frac{- 6.72}{32.61})