tangent
/'tændʤənt/
Học thuậtThân thiện
Definition
- Noun:
- A straight line that touches a curve at a single point without crossing it: In geometry, a tangent is a line that just touches a curve or surface at one point, sharing the same direction as the curve at that point of contact.
- The ratio of the side opposite to the side adjacent to a given angle in a right-angled triangle: In trigonometry, the tangent of an acute angle is a specific numerical ratio defined within a right triangle.
Usage and Examples
- Geometric Meaning:
- The line drawn from the center of the circle to the point of tangency is perpendicular to the tangent.
- The graph of the function has a horizontal tangent at its maximum point.
- Trigonometric Meaning:
- To find the height of the tree, we calculated the tangent of the angle of elevation.
- In the equation,
tan(θ)represents the tangent of angle theta.
Advanced Usage
- To go off on a tangent: This idiom means to suddenly start talking or thinking about a completely new, different, or unrelated subject.
- The professor went off on a tangent about his vacation, forgetting all about the lecture topic.
- Her mind tends to go off on a tangent during meetings.
Variants and Related Words
- Tangential (adjective): Merely touching or slightly connected; only superficially relevant.
- His comment was only tangential to the main discussion.
- Tangency (noun): The state of being tangent; the point of contact.
- The point of tangency between the circle and the line.
Synonyms
- Touching line (for the geometric sense).
- Trigonometric ratio (for the mathematical function sense).
Related Idioms
- Fly off at a tangent: An alternative phrasing for "go off on a tangent," meaning to diverge abruptly from a course of action or thought.
- He has a habit of flying off at a tangent in the middle of a conversation.
Noun
- ratio of the opposite to the adjacent side of a right-angled triangle
- a straight line or plane that touches a curve or curved surface at a point but does not intersect it at that point