Nothing "happens". You simply have an angle that is an odd multiple of pi radians.
-pi/2 and pi/2
Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.
The arc tangent is the recicple of the tangent which is also known as the cotangent. The tangent of π/2 is undefined, thus the cotangent would be zero.
Because it tends to infinity. Additionally, tangent can be expressed as sin theta divided by cos theta. The sine of 90 is 1. The cosine of 90 is 0. That would be 1 divided by 0, or division by zero; which is undefined.
The tangent of infinity is undefined because it is not a real number. The tangent function is defined as the ratio of the side opposite a given angle to the side adjacent to the angle in a right triangle. Since infinity is an abstract concept which has no physical representation, it is not possible to measure the sides of a triangle with an infinite length. Therefore, the tangent of infinity is undefined.
Yes. the tangents of odd multiples of pi/2 radians are not defined.
The radius and the tangent are perpendicular at the point on the circle where they meet.
then the slope is x=y. there is no slope.
It's not. The tangent of 180 degrees is zero. Consider tan(x) = sin(x)/cos(x). When x = 180 degrees, sin(x) = 0 and cos(x) = -1 and so tan(x) = 0
"Division by zero is undefined" is the result on a calculator.
Everytime you determine on your calculators the tangent of 90 degrees, it returns an electron overflow equivalent to a machine-shriek. This is due to the fact that the formula attempted to divide by zero, thus, the result of TANGENT of 90 degrees is UNDEFINED(Division By ZERO is UNDEFINED/not allowed). All lines following this formula is parallel to the y-axis, including the line on the y-axis itself. Hence, point of tangency is impossible to define since parallel lines NEVER MEET.
The answer would be "undefined" as there is no way to divide a number by zero (0).