What is the limit as x approaches (5pi)/6 of sin(x) ?

The limit as x approaches (5pi)/6 of sin(x) is 1/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches (5pi)/6 of sin(x)

x \to \frac{5 π}{6} lim (sin (x))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to \frac{5 π}{6} lim (sin (x))

Plug in the value

x = \frac{5 π}{6}

= sin (\frac{5 π}{6})

Use the following trivial identity:

sin (\frac{5 π}{6}) = \frac{1}{2}

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{d y}{d x} = (x y)^{2}, y (0) = 1

\int \frac{x ^{5}}{x ^{6} + 2} d x

x \to 9 lim (\frac{1}{( x - 9 ) ^{3}})

7 cos (7 x), 7 - 7 cos (7 x)

\int sec^{9} (x) tan (x) d x

What is the limit as x approaches (5pi)/6 of sin(x) ?
The limit as x approaches (5pi)/6 of sin(x) is 1/2