Definition of tangent in US English:



  • 1A straight line or plane that touches a curve or curved surface at a point, but if extended does not cross it at that point.

    • ‘And yes you can have a tangent of a tangent, although it requires the first one to be a curve in the plane perpendicular to the original circle [although some people may argue about the maths of this].’
    • ‘Note that this curvature is the inverse of the radius of a circle tangent to the neutral line at this point.’
    • ‘At a variable point on the curve the coordinates consisted of the tangent to the curve, the principal normal and the binormal.’
    • ‘The line of fall is the line tangent to the trajectory at the level point.’
    • ‘This highly successful subject deals with rates of change at instants of time by calculating the gradient of the tangent to a curve.’
    • ‘The maximum range velocity is derived graphically by drawing a tangent from the origin to the U-shaped power curve for flight.’
    • ‘One of his most important results explains how the 28 double tangents of the plane quadric are related to the 27 straight lines of the cubic surface.’
    • ‘He also shows how to draw a tangent to three given lines.’
    • ‘This was estimated by taking the tangent of each point of the curve.’
    • ‘He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point.’
    • ‘Furthermore, to keep the smoothness we assume that the lines are tangents to the circles.’
    • ‘However, Newton's approach, based on a decomposition of motion along the tangent and along the normal to the orbital curve, was missing an essential ingredient.’
    • ‘Though the lines are the same we the viewer are persuaded to believe that the outward stretching tangents make the line with convexity appear longer.’
    • ‘The tangents to the curve at the origin make angles of 60 with the x-axis.’
    • ‘It is the only way they could determine instantaneous velocity and the slope of a tangent to a curve - both, incidentally, with very practical applications.’
    • ‘He noticed that he could draw three straight lines, or tangents, that each touched all three circles.’
    • ‘He applied this method in determining tangents to curves and centres of gravity.’
    • ‘Since normals to a straight line never intersect and tangents coincide with the curve, evolutes, involutes and pedal curves are not too interesting.’
    • ‘Thus they visit the classic marginal-value theorem and its graphical solution by constructing a tangent to the mean gain curve.’
    • ‘Alternatively an involute can be thought of as any curve orthogonal to all the tangents to a given curve.’
  • 2A completely different line of thought or action.

    ‘he quickly went off on a tangent about wrestling’
    • ‘We are taking a little bit of a different tangent.’
    • ‘He always misbehaved, and went off at tangents and I had to bring him in line many times.’
    • ‘First, the writer needs to get his facts straight before he goes off on a tangent like that.’
    • ‘First, you need to get your facts straight before you go off on a tangent like that.’
    • ‘However, that's so not the point, I am the queen of subject changes and irrelevant tangents, but tangents are what make life interesting right?’
    • ‘Otherwise, people will start going off on different tangents, and you can't have that.’
    • ‘And so the corporates have inevitably led the Internet and its hopes on a different, money-based tangent leaving the dreamers behind, a little richer and a little wiser.’
    • ‘Did have a bit of a Monty Python moment in my Taxation tutorial today, tutor bloke was off at a bit of a tangent as per normal talking about careers in tax and regaled us with a tale about one of his mates who works for a big tax firm.’
    • ‘Those of us who have absorbed these ideas without question should pause for reflection before modern deviants branch off at further tangents and we lose the connection with first principles entirely.’
    • ‘Too many people posting on this site are showing tendencies to go off on tangents which cumulatively waste years of learning time.’
    • ‘She's way too excited to tell you about EVERYTHING, and often goes off on wild tangents and digressions just to get out a pretty straightforward tale.’
    • ‘He breaks off, perhaps uncomfortable with this line of questioning, and scoots off at a tangent.’
    • ‘If you are so-inclined, you can go off in a thousand tangents and cover an enormous range of topics.’
    • ‘Thankfully, he went off on a different tangent.’
    • ‘If I could just add perhaps on a slightly different tangent, that the Business Council conducted some research about what people's views of the economy and the society were not long ago.’
    • ‘Look at that, we started with the opening credits and I went off on a tangent.’
    • ‘The discussion then went off on a tangent, to the question of how many spheres of equal size could rotate around a central ball of the same size.’
    • ‘Ideas are slowly turned over and puzzled with, and the topic at hand may unintentionally meander off on tangents far away from the original point, wrapped in unusual phrases and reflections.’
    • ‘The chair went one way, she went another the and keyboard headed off at a completely different tangent.’
    • ‘Filtered through his camera lens, the story veers off on eccentric tangents.’
  • 3Mathematics
    The trigonometric function that is equal to the ratio of the sides (other than the hypotenuse) opposite and adjacent to an angle in a right triangle.

    • ‘The trogonometric results include tables of sines and tangents given at 1 intervals.’
    • ‘The proof needs another formula about tangents of angles that we have not covered on the Pi and the Fibonacci Numbers page.’
    • ‘I can't tell the difference between radians, tangents, cotangents, secants, etc.’
    • ‘The first tabulates logarithms of the sine, cosine, tangent and cotangent functions at 1 intervals and shows how to solve triangles using logarithmic functions.’
    • ‘If the tangent of an angle is a/b then the cotangent of that angle is b/a.’


  • (of a line or plane) touching, but not intersecting, a curve or curved surface.

    • ‘In addition, each circle is divided into 8 regions, by adding 3 tangent circles.’
    • ‘Now the tangent line is much easier to visualize. Notice that the tangent line is at a right angle to the aiming line.’
    • ‘Water contact angle refers to the angle between the tangent plane of the liquid surface and the tangent plane of the solid surface at any point along the line of contact.’
    • ‘In particular he constructed the tangent plane and exhibited the surface as an envelope of planes.’
    • ‘Therefore, we say the gradient of the tangent line is 2x, although in this case we knew that already.’
    • ‘Let P be a point outside a circle, let PA be a tangent line, and let PBC be a secant line.’
    • ‘We can never fit a straight tangent line to the curve at the point.’
    • ‘The physical straight lines we draw are not straight; a physical tangent line does not really touch a circle at a point.’
    • ‘Smooth infinitesimal analysis embodies a concept of intensive magnitude in the form of infinitesimal tangent vectors to curves.’
    • ‘Many of them feature drawings and problems that concern tangent circles.’
    • ‘The students are then asked to identify perpendicular cross sections of maximal and minimal curvature using coordinates taken essentially from the tangent plane.’
    • ‘In case the boundary is continuously differentiable at p, we may take this line to be the tangent line to the boundary.’
    • ‘A further reduction was accomplished by using the tangent plane of the surface at a given point as the standard plane of reference (instead of the xy-plane).’
    • ‘Instead, we use the radical plane, defined by the property that any point on it will have equal lengths of tangent line segments to the two atoms.’
    • ‘In 1802 he gave the first solution to the problem of describing in a triangle three circumferences that are mutually tangent, each of which touches two sides of the triangle, the so-called Malfatti problem.’
    • ‘Construct two tangent circles 1 and 2 and the line L through their centers.’
    • ‘The midpoints of segments AM lie directly on the tangent lines.’
    • ‘He drew the diagrams exactly as he had done all of his life, taking great care to make the circles perfectly round and the tangent lines specifically long.’
    • ‘The Kummer surface has 16 isolated conical double points and 16 singular tangent planes and was published in 1864.’
    • ‘To understand this notion fully requires understanding tangent spaces, computing with vector fields, and working with bracket products of vector fields.’


Late 16th century (in tangent (sense 3 of the noun) and as an adjective): from Latin tangent- ‘touching’, from the verb tangere.