Tangent

How it is used

Two meanings: in trigonometry, tan x = sin x / cos x (the 'TOA' in SOH CAH TOA); in geometry and calculus, 'the tangent to the curve at a point' has the same slope as the curve there.

Example sentences

1. The tangent of 45 degrees is exactly 1.

2. Find the equation of the tangent to y = x² at the point (1, 1).

Common collocations

• tangent to the curve
• tangent line
• tangent of an angle
• go off on a tangent

Related terms

• sineIn a right triangle, the ratio of the side opposite an angle to the hypotenuse; it is written sin, so sin 30° = 0.5.
• cosineIn a right triangle, the ratio of the side next to an angle (the adjacent side) to the hypotenuse; it is written cos, so cos 60° = 0.5.
• derivativeA function that gives the rate of change of another function at each point, which is the slope of its graph there; the derivative of x² is 2x.
• slopeA number that measures how steep a line is: the change in y divided by the change in x between any two points on the line.

More terms: Trigonometry

• hypotenuse
• radian