What is the value of 5+5cos((3pi)/4) ?

The value of 5+5cos((3pi)/4) is 5-(5sqrt(2))/2

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5+5cos((3pi)/4)

5 + 5 cos (\frac{3 π}{4})

5 - \frac{5 2}{2}

Decimal Notation

1.46446 \dots

Solution steps

5 + 5 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}

= 5 + 5 (- \frac{2}{2})

Simplify

5 + 5 (- \frac{2}{2}) : 5 - \frac{5 2}{2}

5 + 5 (- \frac{2}{2})

Remove parentheses:

(- a) = - a

= 5 - 5 \cdot \frac{2}{2}

Multiply

5 \cdot \frac{2}{2} : \frac{5 2}{2}

5 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 5}{2}

= 5 - \frac{5 2}{2}

= 5 - \frac{5 2}{2}

sin^{3} (\frac{1}{2} π)

81 (cos (\frac{3 π}{8}) + i sin (\frac{3 π}{8}))

6 \cdot sin (\frac{π}{4})

tan (\frac{9}{4} π)

arcsin (\frac{1}{15})

What is the value of 5+5cos((3pi)/4) ?
The value of 5+5cos((3pi)/4) is 5-(5sqrt(2))/2