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

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

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5sqrt(2)cos(pi/4)

52 cos (\frac{π}{4})

5

Solution steps

52 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}

= 52 \frac{2}{2}

Simplify

52 \frac{2}{2} : 5

52 \frac{2}{2}

Multiply fractions:

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

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

2 \cdot 52 = 10

2 \cdot 52

Apply radical rule:

a a = a

22 = 2

= 5 \cdot 2

Multiply the numbers:

5 \cdot 2 = 10

= 10

= \frac{10}{2}

Divide the numbers:

\frac{10}{2} = 5

= 5

= 5

arctan (\frac{12}{35})

sin (arcsin (\frac{π}{4}))

sin (2 arccos (- \frac{5}{13}))

cos (\frac{π}{4}) - cos (0)

80 \cdot cos (2 0^{\circ})