A2C Glossary

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Algebra 2 Connections Glossary

tangent
	In a right triangle (at right) the ratio is known as the tangent of an acute angle. At right, since the side of length b is opposite angle B and the side length a is adjacent to (or next to) angle B. The function where (x, y) are the coordinates of the point on the unit circle where the radius makes an angle of θ with the positive horizontal axis. (pp. 405, 407)
tangent function
	For any real number θ, the tangent of θ, denoted tanθ, is the slope of the line containing the ray which represents a rotation of θ radians in standard position. The general equation for the tangent function is y = atanb(x − h) + k. This function has period of , vertical asymptotes at for n = 1, 2, ..., , horizontal shift h, and vertical shift k. (p. 405)
tangent inverse
	(tan⁻¹x) Read as the inverse of tangent x, tan⁻¹x is the measure of the angle that has tangent x. We can also write y = arctan x . Note that the notation refers to the inverse of the tangent function, not . Because y = tan⁻¹x is equivalent to x = tan y and there are infinitely many angles y such that tan y = x , the inverse function is restricted to select the principal value of y such that . The graph of the inverse tangent function is at right. (p. 679)
term

term number
	A single number, variable, or product of numbers and variables. A monomial is a term. Also a component of a sequence. (p. 75)
	In a sequence, a number that gives the position of a term in the sequence. A replacement value for the independent variable in a function that determines the sequence. See “sequences.” (p. 92)
terminal ray
	When an angle of rotation is drawn in standard position, the positive x-axis is called the initial ray and the ray that determines the angle is called the terminal ray. (p. 407) See “angle.”
theoretical probability

transverse axis
	A probability calculation based on counting possible outcomes. (p. 540)
	In a hyperbola, the line connecting the vertices of the two branches. (p. 585) See “hyperbola.”
tree diagram (or model)
	Tree diagrams are useful for representing possible outcomes of probability experiments. For example, the tree diagram at right represents the possible outcomes when a coin is flipped twice. (pp. 497, 502)

triangular numbers
	The terms of the sequence 0, 1, 3, 6, 10, … are known as the triangular numbers. These numbers are called triangular because they count the number of points in a sequence of triangular patterns. Each number also represents the sum of the first n integers (n ≥ 0).
trigonometric ratios
	(p. 28) See “sine,” “cosine,” “tangent,” “secant,” “cosecant,” and “cotangent.”
triple root
	A root of a function that occurs exactly three times. If an expression of the form (x − a)³ is a factor of a polynomial, then the polynomial has a triple root at x = a . The graph of the polynomial has an inflection point at x = a . (p. 446)