# is tan 90 undefined or infinity

Shubham Singh
199 Points
8 years ago
it is not defined.
it is said to be infinity because tan 90 approaches a very high value which can not be calculated.
SRIPHANI VARDHAN BELLAMKONDA
21 Points
8 years ago
We already know that tan(90)=sin(90) / cos(90). Sin(90)=1, and Cos(90)=0.
so tan(90)=1/0.
1/1=1
1/0.1=10
1/0.01=100
1/0.001=1000
as u can see the value increases as the denominator’s value decreases. now we can use inductive reasoning to conclude that tan(90) is infinity. However some people disagree that the value of 1/0 is indefined. It is up to u to decide whether to follow  that 1/0 is infinety or u can be those who say that 1/0 is undefined.
Hope this helps!!

34 Points
8 years ago
tan 90 = sin 90/cos 90
=> tan 90 = 1/0 , which is not defined (or undefined).
2061 Points
8 years ago
In a right triangle, if the reference angle is also 90°, then the opposite leg and the hypotenuse run parallel to one another.... and the opposite (complimentary) angle would be 0°, meaning that the opposite side and the hypotenuse overlap. The overlap, as well as the two 90° base angles, would define this to be an isosceles triangle... and the hypotenuse and the opposite sides would be equal. The only type of isosceles right triangle in existence is the 45-45-90, not the 90-90-0. The hypotenuse is supposed to be the longest side, but it is not. One might even argue that the opposite side is infinitely long.

This would not be a real triangle.
shubham sharda
360 Points
8 years ago
It is not defined.