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

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

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4+3cos(pi/4)

4 + 3 cos (\frac{π}{4})

4 + \frac{3 2}{2}

Decimal Notation

6.12132 \dots

Solution steps

4 + 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}

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

Simplify

4 + 3 \cdot \frac{2}{2} : 4 + \frac{3 2}{2}

4 + 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}

= 4 + \frac{3 2}{2}

= 4 + \frac{3 2}{2}

cos (6 1^{\circ}) + sin (2 9^{\circ})

- 2 tan (0) sec^{2} (0)

arccos (0.6875)

sin (\frac{1}{( \frac{2}{5 π} )})

csch (ln (3))