What is the value of sin(1/5 ((5pi)/6))+2 ?

The value of sin(1/5 ((5pi)/6))+2 is 5/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(1/5 ((5pi)/6))+2

sin (\frac{1}{5} (\frac{5 π}{6})) + 2

\frac{5}{2}

Decimal Notation

2.5

Solution steps

sin (\frac{1}{5} (\frac{5 π}{6})) + 2

= sin (\frac{1}{5} \cdot \frac{5 π}{6}) + 2

Simplify:

\frac{1}{5} \cdot \frac{5 π}{6} = \frac{π}{6}

\frac{1}{5} \cdot \frac{5 π}{6}

Multiply fractions:

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

= \frac{1 \cdot 5 π}{5 \cdot 6}

Cancel the common factor:

5

= \frac{1 π}{6}

Multiply:

1 π = π

= \frac{π}{6}

= sin (\frac{π}{6}) + 2

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

sin (\frac{π}{6})

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{1}{2}

= \frac{1}{2} + 2

Simplify

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

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

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

cos (arcsin (\frac{1}{6}))

sec (1 8^{\circ})

cos (18 0^{\circ}) - sin (18 0^{\circ})

cos (\frac{30}{2})

What is the value of sin(1/5 ((5pi)/6))+2 ?
The value of sin(1/5 ((5pi)/6))+2 is 5/2