What is the limit as x approaches pi/2 of (cos(x))/(cot(x)) ?

The limit as x approaches pi/2 of (cos(x))/(cot(x)) is 1

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limit as x approaches pi/2 of (cos(x))/(cot(x))

x \to \frac{π}{2} lim (\frac{cos ( x )}{cot ( x )})

1

Solution steps

x \to \frac{π}{2} lim (\frac{cos ( x )}{cot ( x )})

Express with sin, cos

= x \to \frac{π}{2} lim (sin (x))

Plug in the value

x = \frac{π}{2}

= sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

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}

= 1

\frac{\partial}{\partial x} (x y sin (x y))

\int \frac{e ^{x}}{4 + e ^{x}} d x

\frac{d}{d t} (t^{2} + 1)

\frac{d y}{d t} = \frac{t ^{2}}{y ( 1 + t ^{3} )}

\int_{3}^{4} \frac{x}{8} d x

What is the limit as x approaches pi/2 of (cos(x))/(cot(x)) ?
The limit as x approaches pi/2 of (cos(x))/(cot(x)) is 1