What is the limit as x approaches (3pi)/4 of sin(x) ?

The limit as x approaches (3pi)/4 of sin(x) is (sqrt(2))/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 (3pi)/4 of sin(x)

x \to \frac{3 π}{4} lim (sin (x))

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

x \to \frac{3 π}{4} lim (sin (x))

Plug in the value

x = \frac{3 π}{4}

= sin (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{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{2}{2}

x \to 0 lim (2 x^{3 x})

x \to 0 lim ((1 - 9 x)^{\frac{5}{x}})

x \to 2 + lim (\frac{x - 3}{x ^{2} - 2})

x \to 2 lim (∣ x - 2 ∣)

x \to 0 lim (2^{x} - 1)

What is the limit as x approaches (3pi)/4 of sin(x) ?
The limit as x approaches (3pi)/4 of sin(x) is (sqrt(2))/2