What is the value of 8cos((3pi)/4) ?

The value of 8cos((3pi)/4) is -4sqrt(2)

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8cos((3pi)/4)

8 cos (\frac{3 π}{4})

- 42

Decimal

- 5.65685 \dots

Solution steps

8 cos (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

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{2}{2}

= 8 (- \frac{2}{2})

Simplify

8 (- \frac{2}{2}) : - 42

8 (- \frac{2}{2})

Remove parentheses:

(- a) = - a

= - 8 \cdot \frac{2}{2}

Multiply fractions:

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

= - \frac{2 \cdot 8}{2}

Divide the numbers:

\frac{8}{2} = 4

= - 42

= - 42