What is the value of 4.2*1.3*sin(75)-4.9*2.15*sin(60) ?

The value of 4.2*1.3*sin(75)-4.9*2.15*sin(60) is (273(sqrt(6)+sqrt(2)))/(200)-(2107sqrt(3))/(400)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4.21.3sin(75)-4.92.15sin(60)

Solution

4.2 \cdot 1.3 \cdot sin (7 5^{\circ}) - 4.9 \cdot 2.15 \cdot sin (6 0^{\circ})

Solution

\frac{273 ( 6 + 2 )}{200} - \frac{2107 3}{400}

Decimal Notation

- 3.84962 \dots

Solution steps

4.2 \cdot 1.3 sin (7 5^{\circ}) - 4.9 \cdot 2.15 sin (6 0^{\circ})

= \frac{21}{5} \cdot \frac{13}{10} sin (7 5^{\circ}) - \frac{49}{10} \cdot \frac{43}{20} sin (6 0^{\circ})

Rewrite using trig identities:

sin (7 5^{\circ}) = \frac{6 + 2}{4}

sin (7 5^{\circ})

Rewrite using trig identities:

sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

sin (7 5^{\circ})

Write

sin (7 5^{\circ})

sin (4 5^{\circ} + 3 0^{\circ})

= sin (4 5^{\circ} + 3 0^{\circ})

Use the Angle Sum identity:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

= sin (4 5^{\circ}) cos (3 0^{\circ}) + cos (4 5^{\circ}) sin (3 0^{\circ})

Use the following trivial identity:

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

sin (4 5^{\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{2}{2}

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}

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}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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{1}{2}

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

Simplify

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} : \frac{6 + 2}{4}

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

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{4}

\frac{2}{2} \cdot \frac{3}{2}

Multiply fractions:

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

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{2 3}{4}

Simplify

23 : 6

23

Apply radical rule:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= \frac{6}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

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

Multiply fractions:

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

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

Multiply:

2 \cdot 1 = 2

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{6}{4} + \frac{2}{4}

Apply rule

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

= \frac{6 + 2}{4}

= \frac{6 + 2}{4}

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}

= \frac{21}{5} \cdot \frac{13}{10} \cdot \frac{6 + 2}{4} - \frac{49}{10} \cdot \frac{43}{20} \cdot \frac{3}{2}

Simplify

\frac{21}{5} \cdot \frac{13}{10} \cdot \frac{6 + 2}{4} - \frac{49}{10} \cdot \frac{43}{20} \cdot \frac{3}{2} : \frac{273 ( 6 + 2 )}{200} - \frac{2107 3}{400}

\frac{21}{5} \cdot \frac{13}{10} \cdot \frac{6 + 2}{4} - \frac{49}{10} \cdot \frac{43}{20} \cdot \frac{3}{2}

\frac{21}{5} \cdot \frac{13}{10} \cdot \frac{6 + 2}{4} = \frac{273 ( 6 + 2 )}{200}

\frac{21}{5} \cdot \frac{13}{10} \cdot \frac{6 + 2}{4}

Multiply fractions:

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

= \frac{21 \cdot 13 ( 6 + 2 )}{5 \cdot 10 \cdot 4}

Multiply the numbers:

21 \cdot 13 = 273

= \frac{273 ( 6 + 2 )}{5 \cdot 10 \cdot 4}

Multiply the numbers:

5 \cdot 10 \cdot 4 = 200

= \frac{273 ( 6 + 2 )}{200}

\frac{49}{10} \cdot \frac{43}{20} \cdot \frac{3}{2} = \frac{2107 3}{400}

\frac{49}{10} \cdot \frac{43}{20} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{49 \cdot 43 3}{10 \cdot 20 \cdot 2}

Multiply the numbers:

49 \cdot 43 = 2107

= \frac{2107 3}{10 \cdot 20 \cdot 2}

Multiply the numbers:

10 \cdot 20 \cdot 2 = 400

= \frac{2107 3}{400}

= \frac{273 ( 6 + 2 )}{200} - \frac{2107 3}{400}

= \frac{273 ( 6 + 2 )}{200} - \frac{2107 3}{400}

Popular Examples

tan((11pi)/6-(7pi)/4)

tan (\frac{11 π}{6} - \frac{7 π}{4})

0.1851*9.8*cos(11.34)

0.1851 \cdot 9.8 \cdot cos (11.3 4^{\circ})

cos^2(pi/6)+sin^2(pi/6)

cos^{2} (\frac{π}{6}) + sin^{2} (\frac{π}{6})

cos(30)4

cos (3 0^{\circ}) 4

arctan(-1.33)

arctan (- 1.33)

Frequently Asked Questions (FAQ)

What is the value of 4.2*1.3*sin(75)-4.9*2.15*sin(60) ?
The value of 4.2*1.3*sin(75)-4.9*2.15*sin(60) is (273(sqrt(6)+sqrt(2)))/(200)-(2107sqrt(3))/(400)