What is the value of 1.5(2-cos(120)) ?

The value of 1.5(2-cos(120)) is 15/4

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1.5(2-cos(120))

1.5 (2 - cos (12 0^{\circ}))

\frac{15}{4}

Decimal Notation

3.75

Solution steps

1.5 (2 - cos (12 0^{\circ}))

= \frac{3}{2} (2 - cos (12 0^{\circ}))

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

cos (12 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{1}{2}

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

Simplify

\frac{3}{2} (2 - (- \frac{1}{2})) : \frac{15}{4}

\frac{3}{2} (2 - (- \frac{1}{2}))

Apply rule

- (- a) = a

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

Join

2 + \frac{1}{2} : \frac{5}{2}

2 + \frac{1}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 2 + 1 = 5

2 \cdot 2 + 1

Multiply the numbers:

2 \cdot 2 = 4

= 4 + 1

Add the numbers:

4 + 1 = 5

= 5

= \frac{5}{2}

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

Multiply fractions:

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

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

Multiply the numbers:

3 \cdot 5 = 15

= \frac{15}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{15}{4}

= \frac{15}{4}

520 cos (4 5^{\circ})

11 sin (4 1^{\circ})

4 sin^{2} (6 0^{\circ}) - csc (3 0^{\circ})

- 3 cos (4 5^{\circ})

arctan (\frac{- 120}{- 27})