What is the value of 6+3cos(pi/4) ?

The value of 6+3cos(pi/4) is 6+(3sqrt(2))/2

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6+3cos(pi/4)

6 + 3 cos (\frac{π}{4})

6 + \frac{3 2}{2}

Decimal Notation

8.12132 \dots

Solution steps

6 + 3 cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{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}

= 6 + 3 \cdot \frac{2}{2}

Simplify

6 + 3 \cdot \frac{2}{2} : 6 + \frac{3 2}{2}

6 + 3 \cdot \frac{2}{2}

Multiply

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

3 \cdot \frac{2}{2}

Multiply fractions:

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

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

= 6 + \frac{3 2}{2}

= 6 + \frac{3 2}{2}

20 \cdot sin (5 0^{\circ})

tan (- 8)

2 \cdot 0.35 \cdot 1 0^{- 9} \cdot sin (6.43)

tan (arctan (\frac{1}{4}) + arctan (\frac{3}{5}))

arcsin (854907)