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.
Chat with our AI personalities
The tangent of 42 degrees is approximately 0.9004. To calculate this, you can use a scientific calculator or a trigonometric table. The tangent function in trigonometry is defined as the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle in a right triangle.
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. ]