At each point x on the differentiable manifold M, the tangent space consists of all vectors tangent to M at x and forms an n-dimensional vector space.

At the lecture, she drew the inflectional tangent to show how the curve changes concavity.

The tangent line at that point provides the best linear approximation of the curve near the point.

To determine the angle in the triangle, he used the inverse tangent of the ratio of the opposite side to the adjacent side.

During the workshop, the professor used several examples to show how tangent planes approximate a surface near a point.

To calculate the unknown sides of the triangle, she applied the law of tangents, which relates the tangents of two angles to the lengths of the opposing sides.

In advanced neural network layers, hyperbolic tangents are often used as activation functions to introduce nonlinearity.

The linguist mapped inflectional tangents across the corpus to track morphological shifts.

The professor demonstrated how inverse tangents can be used to determine angles in the coordinate plane.

Whenever we start discussing budgets, Mark tends to fly off at a tangent and tell stories about his college days.