What is the value of 60sqrt(2)cos(45) ?

The value of 60sqrt(2)cos(45) is 60

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60sqrt(2)cos(45)

602 cos (4 5^{\circ})

60

Solution steps

602 cos (4 5^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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}

= 602 \frac{2}{2}

Simplify

602 \frac{2}{2} : 60

602 \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 60 2}{2}

2 \cdot 602 = 120

2 \cdot 602

Apply radical rule:

a a = a

22 = 2

= 60 \cdot 2

Multiply the numbers:

60 \cdot 2 = 120

= 120

= \frac{120}{2}

Divide the numbers:

\frac{120}{2} = 60

= 60

= 60

tan (\frac{7 π}{9})

arctan (\frac{12.1024}{12})

arccos (cos (\frac{2 π}{3})) + arcsin (sin (\frac{2 π}{3}))

tan (7 1^{\circ})

5 + 4 cos (- \frac{π}{4})