What is the limit as x approaches pi/4 of-cos(x) ?

The limit as x approaches pi/4 of-cos(x) is -(sqrt(2))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches pi/4 of-cos(x)

x \to \frac{π}{4} lim (- cos (x))

- \frac{2}{2}

Decimal

- 0.70710 \dots

Solution steps

x \to \frac{π}{4} lim (- cos (x))

Plug in the value

x = \frac{π}{4}

= - cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} 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}

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