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

x \to 0 lim (x^{3} + 3 x^{2} - x + 1)

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

x \to \frac{x}{2} lim (3 sec (x) - 3 tan (x))

x \to 3 lim (\frac{x ^{2} + 40 - 7}{x - 3})

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