What is the value of (3/2)((9.8)/(0.4))(1-sin(60)+cos(60)) ?

The value of (3/2)((9.8)/(0.4))(1-sin(60)+cos(60)) is (147(3-sqrt(3)))/8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(3/2)((9.8)/(0.4))(1-sin(60)+cos(60))

Solution

(\frac{3}{2}) (\frac{9.8}{0.4}) (1 - sin (6 0^{\circ}) + cos (6 0^{\circ}))

Solution

\frac{147 ( 3 - 3 )}{8}

Decimal Notation

23.29856 \dots

Solution steps

(\frac{3}{2}) (\frac{9.8}{0.4}) (1 - sin (6 0^{\circ}) + cos (6 0^{\circ}))

= \frac{3}{2} \cdot \frac{\frac{49}{5}}{\frac{2}{5}} (1 - sin (6 0^{\circ}) + cos (6 0^{\circ}))

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 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} \cdot \frac{\frac{49}{5}}{\frac{2}{5}} (1 - \frac{3}{2} + \frac{1}{2})

Simplify

\frac{3}{2} \cdot \frac{\frac{49}{5}}{\frac{2}{5}} (1 - \frac{3}{2} + \frac{1}{2}) : \frac{147 ( 3 - 3 )}{8}

\frac{3}{2} \cdot \frac{\frac{49}{5}}{\frac{2}{5}} (1 - \frac{3}{2} + \frac{1}{2})

Combine the fractions

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

Apply rule

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

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

= \frac{3}{2} \cdot \frac{\frac{49}{5}}{\frac{2}{5}} (\frac{1 - 3}{2} + 1)

\frac{\frac{49}{5}}{\frac{2}{5}} = \frac{49}{2}

\frac{\frac{49}{5}}{\frac{2}{5}}

Divide fractions:

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

= \frac{49 \cdot 5}{5 \cdot 2}

Cancel the common factor:

5

= \frac{49}{2}

= \frac{3}{2} \cdot \frac{49}{2} (\frac{1 - 3}{2} + 1)

Multiply fractions:

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

= \frac{3 \cdot 49 ( 1 + \frac{- 3 + 1}{2} )}{2 \cdot 2}

Multiply the numbers:

3 \cdot 49 = 147

= \frac{147 ( \frac{1 - 3}{2} + 1 )}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{147 ( \frac{1 - 3}{2} + 1 )}{4}

Join

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

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

Convert element to fraction:

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

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

1 \cdot 2 - 3 + 1 = 3 - 3

1 \cdot 2 - 3 + 1

Multiply the numbers:

1 \cdot 2 = 2

= 2 - 3 + 1

Add the numbers:

2 + 1 = 3

= 3 - 3

= \frac{3 - 3}{2}

= \frac{147 \cdot \frac{3 - 3}{2}}{4}

Multiply

147 \cdot \frac{3 - 3}{2} : \frac{147 ( 3 - 3 )}{2}

147 \cdot \frac{3 - 3}{2}

Multiply fractions:

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

= \frac{( 3 - 3 ) \cdot 147}{2}

= \frac{\frac{147 ( 3 - 3 )}{2}}{4}

Apply the fraction rule:

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

= \frac{( 3 - 3 ) \cdot 147}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{147 ( 3 - 3 )}{8}

= \frac{147 ( 3 - 3 )}{8}

Popular Examples

cos(0.68)

cos (0.68)

cos(150)-sin(240)+tan(300)

cos (15 0^{\circ}) - sin (24 0^{\circ}) + tan (30 0^{\circ})

arctan((-(sqrt(3))/2)/(1/2))

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

arccos(-0.05)

arccos (- 0.05)

cos(0.99)

cos (0.99)

Frequently Asked Questions (FAQ)

What is the value of (3/2)((9.8)/(0.4))(1-sin(60)+cos(60)) ?
The value of (3/2)((9.8)/(0.4))(1-sin(60)+cos(60)) is (147(3-sqrt(3)))/8