The cotangent ( cot ⁡ ) (/cot) (cot) The cotangent is the reciprocal of the tangent. It is the ratio of the adjacent side to the opposite side in a right triangle.

For any y=cot(x) y = cot ( x ) , vertical asymptotes occur at x=nπ x = n π , where n is an integer. Use the basic period for y=cot(x) y = cot ( x ) , (0,π) , to find the vertical asymptotes for y=cot(x) y = cot ( x ) .

In your case, the function cot(x) is defined as 1tan(x) , which is cos(x)sin(x) . So, the zeros of the denominator are the ones of the sine function which, periodicity apart, are 0 and π . So, your vertical asymptotes are vertical lines of equations x=0 and x=π .

The vertical asymptotes for y=cot(x) y = cot ( x ) occur at 0 0 , π π , and every πn π n , where n n is an integer.

The cotangent of x is defined to be the cosine of x divided by the sine of x: cot x = cos x sin x . The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

Sine and cosine functions do not have asymptotes.

There are three kinds of asymptotes: horizontal, vertical and oblique. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞.

The vertical asymptotes will occur at those values of x for which the denominator is equal to zero: x2 − 4=0 x2 = 4 x = ±2 Thus, the graph will have vertical asymptotes at x = 2 and x = −2. To find the horizontal asymptote, we note that the degree of the numerator is one and the degree of the denominator is two.

How to Find Horizontal Asymptotes?

1. If the degree of the polynomials both in numerator and denominator is equal, then divide the coefficients of highest degree terms to get the horizontal asymptotes.
2. If the degree of the numerator is less than the degree of the denominator, then the horizontal asymptotes will be y = 0.

a line which approaches nearer to some curve than assignable distance, but, though infinitely extended, would never meet it. Asymptotes may be straight lines or curves. A rectilinear asymptote may be conceived as a tangent to the curve at an infinite distance. Etymology: [Gr. not falling together; ‘a priv.

The following are usually easy to carry out and give important clues as to the shape of a curve:

1. Determine the x and y intercepts of the curve.
2. Determine the symmetry of the curve.
3. Determine any bounds on the values of x and y.
4. If the curve passes through the origin then determine the tangent lines there.

The three rules that horizontal asymptotes follow are based on the degree of the numerator, n, and the degree of the denominator, m. If n < m, the horizontal asymptote is y = 0. If n = m, the horizontal asymptote is y = a/b. If n > m, there is no horizontal asymptote.

The Cartesian curves are the bicircular quartics with two cusps at infinity. They are the curves that can be defined as cyclic curves with a circle as the initial curve (called initial circle). These curves are inverses of Cartesian ovals.

The following steps are taken in the process of curve sketching:

1. Domain. Find the domain of the function and determine the points of discontinuity (if any).
2. Intercepts.
3. Symmetry.
4. Asymptotes.
5. Intervals of Increase and Decrease.
6. Local Maximum and Minimum.
7. Concavity/Convexity and Points of Inflection.
8. Graph of the Function.

Team Desmos All you have to do is click and hold your mouse button down on top of a graph, and you’ll see the closest set of coordinates appear. The trace will stick on points of interest, like maximums, minimums, y-intercepts, roots, and intersections.

Definition: The intersection of a surface with a plane is called the trace of the surface in that plane. Quadric surfaces are characterized by their traces in vertical planes x = k or y = k and horizontal planes z = k. x2 a2 + y2 b2 + z2 c2 = 1 is called an ellipsoid.

Graph Trace lets you move a trace cursor over the points of a graph or plot and displays value information. From the Trace menu, select Graph Trace. The Graph Trace tool appears at the top of the work area, the trace cursor appears, and the cursor coordinates are displayed in the lower right corner.

Traces and 3D Graphing: Definition: The trace of a graph in 3-dimensional space is the intersection of the graph with a single plane. • We often think of a trace as a “shadow” or “cross-section” of the graph when it is “sliced” by a particular plane.

TI-84: Finding Graph Coordinates (Tracing)

1. Press [Trace]. Then use the right and left arrow keys to move along the curve.
2. Use the Up or Down arrow keys to switch functions. Then use the Right and Left arrow keys to trace.
3. Alternatively, [2nd] [CALC] provides a menu of items. Choose “5: intersect”.

The y -intercept of a graph is the point where the graph crosses the y -axis. When the equation of a line is written in slope-intercept form ( y=mx+b ), the y -intercept b can be read immediately from the equation. Example 1: The graph of y=34x−2 has its y -intercept at −2 .