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sin(x)/cos(x)
Limit of the function/ sin(x)/cos(x)

Limit of the function sin(x)/cos(x)

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      /sin(x)\
 lim  |------|
   pi \cos(x)/
x->--+        
   2
lim⁡x→π2+(sin⁡(x)cos⁡(x))\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) 
Limit(sin(x)/cos(x), x, pi/2)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.0-250250
Plot the graph
One‐sided limits [src] 
      /sin(x)\
 lim  |------|
   pi \cos(x)/
x->--+        
   2
lim⁡x→π2+(sin⁡(x)cos⁡(x))\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) 
-oo
−∞-\infty 
= -150.997792488028
      /sin(x)\
 lim  |------|
   pi \cos(x)/
x->---        
   2
lim⁡x→π2−(sin⁡(x)cos⁡(x))\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) 
oo
∞\infty 
= 150.997792488025
= 150.997792488025
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→π2−(sin⁡(x)cos⁡(x))=−∞\lim_{x \to \frac{\pi}{2}^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = -\infty
More at x→pi/2 from the left
lim⁡x→π2+(sin⁡(x)cos⁡(x))=−∞\lim_{x \to \frac{\pi}{2}^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = -\infty
lim⁡x→∞(sin⁡(x)cos⁡(x))\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)
More at x→oo
lim⁡x→0−(sin⁡(x)cos⁡(x))=0\lim_{x \to 0^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0
More at x→0 from the left
lim⁡x→0+(sin⁡(x)cos⁡(x))=0\lim_{x \to 0^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = 0
More at x→0 from the right
lim⁡x→1−(sin⁡(x)cos⁡(x))=sin⁡(1)cos⁡(1)\lim_{x \to 1^-}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}
More at x→1 from the left
lim⁡x→1+(sin⁡(x)cos⁡(x))=sin⁡(1)cos⁡(1)\lim_{x \to 1^+}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right) = \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}
More at x→1 from the right
lim⁡x→−∞(sin⁡(x)cos⁡(x))\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}\right)
More at x→-oo
Numerical answer [src] 
-150.997792488028
-150.997792488028
The graph
Limit of the function sin(x)/cos(x)
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