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

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

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4+(3sqrt(2))/2 cos((3pi)/4)

4 + \frac{3 2}{2} cos (\frac{3 π}{4})

\frac{5}{2}

Decimal Notation

2.5

Solution steps

4 + \frac{3 2}{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}

= 4 + \frac{3 2}{2} (- \frac{2}{2})

Simplify

4 + \frac{3 2}{2} (- \frac{2}{2}) : \frac{5}{2}

4 + \frac{3 2}{2} (- \frac{2}{2})

Remove parentheses:

(- a) = - a

= 4 - \frac{3 2}{2} \cdot \frac{2}{2}

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

\frac{3 2}{2} \cdot \frac{2}{2}

Multiply fractions:

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

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

322 = 6

322

Apply radical rule:

a a = a

22 = 2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

= \frac{6}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{6}{4}

Cancel the common factor:

2

= \frac{3}{2}

= 4 - \frac{3}{2}

Convert element to fraction:

4 = \frac{4 \cdot 2}{2}

= \frac{4 \cdot 2}{2} - \frac{3}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{4 \cdot 2 - 3}{2}

4 \cdot 2 - 3 = 5

4 \cdot 2 - 3

Multiply the numbers:

4 \cdot 2 = 8

= 8 - 3

Subtract the numbers:

8 - 3 = 5

= 5

= \frac{5}{2}

= \frac{5}{2}

\frac{1}{cos ^{2} ( \frac{π}{3} )}

arccos (\frac{5}{9 14})

cos (- 5 0^{\circ})

arcsin (\frac{1}{1.7606})

cos (32.0 1^{\circ})

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