The tangent of 90 degrees is undefined.
Here's why:
The tangent function (tan) in trigonometry is defined as the ratio of the sine function (sin) to the cosine function (cos):
tan(θ) = sin(θ) / cos(θ)
For 90 degrees:
- sin(90°) = 1
- cos(90°) = 0
Therefore:
tan(90°) = 1 / 0
Division by zero is undefined in mathematics. Consequently, the tangent of 90 degrees is undefined. It approaches infinity as the angle approaches 90 degrees.
