Sentence examples for secant from inspiring English sources
noun
A straight line that intersects a curve at two or more points.
In 1569 Gerardus Mercator solved the projection problem by producing his famous world map with the meridians vertical and parallels having increased spacing in proportion to the secant (a trigonometric function) of the latitude.
These relations may also be stated briefly by saying that cosine and secant are even functions (symmetrical about the y-axis), while the other four are odd functions (symmetrical about the origin).
Because division by zero is not allowed, the tangent and secant are not defined for angles the terminal side of which falls on the y-axis, and the cotangent and cosecant are undefined for angles the terminal side of which falls on the x-axis.
A tangent line may be considered the limiting position of a secant line as the two points at which it crosses the curve approach one another.
When the Pythagorean equality x2 + y2 = r2 is divided in turn by r2, x2, and y2, the three squared relations relating cosine and sine, tangent and secant, cotangent and cosecant are obtained.
To obtain the tangent to a curve by this method, Fermat began with a secant through two points a short distance apart and let the distance vanish (see figure).
In this geometric context, the expression gt + gh/2 (or its equivalent [f(t + h) − f(t)]/h) denotes the slope of a secant line connecting the point (t, f(t)) to the nearby point (t + h, f(t + h)) (see figure).
In the limit, with smaller and smaller intervals h, the secant line approaches the tangent line and its slope at the point t.
Using Euclid's results on similar triangles and on secants of circles, he found a relation satisfied by the distances from any point P of a conic to two perpendicular lines, the major axis of the conic and the tangent at an endpoint of the axis.
But neither the teacher-trainees nor their instructor, Michael R. Richardson, a former high school math teacher, showed any sign of fading as he drew circles and secants on the board with colored markers and quizzed them on exponential numbers.
The students in one of the math immersion classes at City College last month seemed to have little problem following their teacher as he moved rapidly through secants, tangents and geometric proofs.
