The tangent of an angle theta is defined as sine(theta) divided by cosine(theta). Since the sine and cosine are Y and X on the unit circle, then tangent(theta) is Y divided by X.
The tangent of a function at a point is the line going through that point which has slope equal to the first deriviative of the function at that point.
Oh, dude, the tangent of 42 degrees is like the ratio of the length of the opposite side to the adjacent side in a right triangle with a 42-degree angle. So, technically, it's the tangent of 42 degrees. But like, who really cares about tangents, am I right?
A rate of change in a variable Y, if not further qualified, is the change in Y for a unit change in time. However, the rate of change may be defined in terms of a unit change in some other variable (X). In graphical terms, the rate of change for a straight line is its gradient whereas for a curve, the rate of change at a point is the gradient of the tangent to the curve (if a tangent can be defined).
Tangent = 0.5
The arc tangent is the recicple of the tangent which is also known as the cotangent. The tangent of π/2 is undefined, thus the cotangent would be zero.
Such a line is called a tangent line or a tangent to the circle. [Tangent is Latin for touching-- a tangent line touches the circle at just one point. ]
Tangent (theta) is defined as sine (theta) divided by cosine (theta). In a right triangle, it is also defined as opposite (Y) divided by adjacent (X).
tangent
tangent
The tangent function will generate a calculator "math error" if the angle in questin is ±90 degrees. For these angles, the tangent function is not defined.
The slope of a line and the tangent of the angle between the positive x-axis and the line are related because the tangent of the angle is defined as the ratio of the y-coordinate and the x-coordinate of some point on the line.
instantaneous
Yes. the tangents of odd multiples of pi/2 radians are not defined.
Tangent
It is a tangent line
Yes. Both are defined on all points other than odd multiples of 90 degrees.
The tangent of infinity is undefined because it is not a real number. The tangent function is defined as the ratio of the side opposite a given angle to the side adjacent to the angle in a right triangle. Since infinity is an abstract concept which has no physical representation, it is not possible to measure the sides of a triangle with an infinite length. Therefore, the tangent of infinity is undefined.
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