What is the value of 5/2 sin((4pi)/3-pi) ?

The value of 5/2 sin((4pi)/3-pi) is (5sqrt(3))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5/2 sin((4pi)/3-pi)

\frac{5}{2} sin (\frac{4 π}{3} - π)

\frac{5 3}{4}

Decimal Notation

2.16506 \dots

Solution steps

\frac{5}{2} sin (\frac{4 π}{3} - π)

Simplify:

\frac{4 π}{3} - π = \frac{π}{3}

\frac{4 π}{3} - π

Convert element to fraction:

π = \frac{π 3}{3}

= \frac{4 π}{3} - \frac{π 3}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{4 π - π 3}{3}

Add similar elements:

4 π - 3 π = π

= \frac{π}{3}

\frac{5}{2} sin (\frac{π}{3}) = \frac{5 sin ( \frac{π}{3} )}{2}

\frac{5}{2} sin (\frac{π}{3})

Multiply fractions:

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

= \frac{5 sin ( \frac{π}{3} )}{2}

= \frac{5 sin ( \frac{π}{3} )}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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{5 \cdot \frac{3}{2}}{2}

Simplify

\frac{5 \cdot \frac{3}{2}}{2} : \frac{5 3}{4}

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

Multiply

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

5 \cdot \frac{3}{2}

Multiply fractions:

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

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

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

Apply the fraction rule:

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

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{5 3}{4}

= \frac{5 3}{4}

π sec (π)

40 \cdot cos (5 3^{\circ})

arcsin (- \frac{π}{3})

sin (4 arcsin (1))

2 sec (6 0^{\circ})

What is the value of 5/2 sin((4pi)/3-pi) ?
The value of 5/2 sin((4pi)/3-pi) is (5sqrt(3))/4