What is the value of 1/2 cos((3pi)/4) ?

The value of 1/2 cos((3pi)/4) is -(sqrt(2))/4

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1/2 cos((3pi)/4)

\frac{1}{2} cos (\frac{3 π}{4})

- \frac{2}{4}

Decimal Notation

- 0.35355 \dots

Solution steps

\frac{1}{2} 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}

= \frac{1}{2} (- \frac{2}{2})

Simplify

\frac{1}{2} (- \frac{2}{2}) : - \frac{2}{4}

\frac{1}{2} (- \frac{2}{2})

Remove parentheses:

(- a) = - a

= - \frac{1}{2} \cdot \frac{2}{2}

Multiply fractions:

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

= - \frac{1 \cdot 2}{2 \cdot 2}

Multiply:

1 \cdot 2 = 2

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

Multiply the numbers:

2 \cdot 2 = 4

= - \frac{2}{4}

= - \frac{2}{4}

arctan (\frac{\frac{3}{2}}{- \frac{1}{2}})

tan (\frac{π}{4} - 0.2) - tan (\frac{π}{4})

tan (arccos (\frac{20}{29}))

9.8 \cdot sin (6 0^{\circ})

cos (2 arcsin (\frac{3}{2}))

What is the value of 1/2 cos((3pi)/4) ?
The value of 1/2 cos((3pi)/4) is -(sqrt(2))/4