What is the value of 0.2(1+cos(30)) ?

The value of 0.2(1+cos(30)) is (2+sqrt(3))/(10)

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0.2(1+cos(30))

0.2 (1 + cos (3 0^{\circ}))

\frac{2 + 3}{10}

Decimal Notation

0.37320 \dots

Solution steps

0.2 (1 + cos (3 0^{\circ}))

= \frac{1}{5} (1 + cos (3 0^{\circ}))

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\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{3}{2}

= \frac{1}{5} (1 + \frac{3}{2})

Simplify

\frac{1}{5} (1 + \frac{3}{2}) : \frac{2 + 3}{10}

\frac{1}{5} (1 + \frac{3}{2})

Multiply fractions:

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

= \frac{1 \cdot ( 1 + \frac{3}{2} )}{5}

1 \cdot (1 + \frac{3}{2}) = 1 + \frac{3}{2}

1 \cdot (1 + \frac{3}{2})

Multiply:

1 \cdot (1 + \frac{3}{2}) = (1 + \frac{3}{2})

= (1 + \frac{3}{2})

Remove parentheses:

(a) = a

= 1 + \frac{3}{2}

= \frac{1 + \frac{3}{2}}{5}

Join

1 + \frac{3}{2} : \frac{2 + 3}{2}

1 + \frac{3}{2}

Convert element to fraction:

1 = \frac{1 \cdot 2}{2}

= \frac{1 \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{1 \cdot 2 + 3}{2}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2 + 3}{2}

= \frac{\frac{2 + 3}{2}}{5}

Apply the fraction rule:

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

= \frac{2 + 3}{2 \cdot 5}

Multiply the numbers:

2 \cdot 5 = 10

= \frac{2 + 3}{10}

= \frac{2 + 3}{10}

4 sin (8)

10 \cdot 12 \cdot sin (3 7^{\circ})

50 sin (66.4 2^{\circ})

sin (2 \cdot 90)

23.47 \cdot sin (\frac{360 ( 284 + 44 )}{365})

What is the value of 0.2(1+cos(30)) ?
The value of 0.2(1+cos(30)) is (2+sqrt(3))/(10)