Chapter 2 - Precalculus

tan (right triangle form)

opposite/adjacent

sin (right triangle form)

opposite/hypotenuse

sec (coordinate form)

radius/horizontal coordinate

csc (coordinate form)

radius/vertical coordinate

cosine

ratio of the adjacent side to the hypotenuse of a right-angled triangle

cotangent

ratio of the adjacent to the opposite side of a right-angled triangle

secant

ratio of the hypotenuse to the adjacent side of a right-angled triangle

cosecant

ratio of the hypotenuse to the opposite side of a right-angled triangle

tangent

ratio of the opposite to the adjacent side of a right-angled triangle

period function

the horizontal distance after which the graph of the function starts repeating itself

reference angle

For any given angle, its reference angle is an acute version of that angle. In standard position, the reference angle is the smallest angle between the terminal side and the x-axis. The values of the trig functions of angle θ are the same as the trig values of the reference angle for θ, give or take a minus sign.

coterminal angles

Two angles in standard position who have identical terminal sides.

adjacent

near or close to but not necessarily touching

sine function

a trigonometric ratio formed by the opposite side divided by the hypotenuse

unit circle

a unit circle is a circle with a unit radius, i.e., a circle whose radius is 1. Frequently, especially in trigonometry, "the" unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane. The unit circle is often denoted S1; the generalization to higher dimensions is the unit sphere.

cos (right triangle form)

adjacent/hypotenuse

cot (right triangle form)

adjacent/opposit

trigonometric functions

are functions of an angle. They are important in the study of triangles and modeling periodic phenomena, among many other applications. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.

cos (coordinate form)

horizontal coordinate/radius

cot (coordinate form)

horizontal coordinate/vertical coordinate

sec (right triangle form)

hypotenuse/adjacent

csc (right triangle form)

hypotenuse/opposite

reciprocal property

if two ratios are equal, then their reciprocals are also equal

hypotenuse

the side of a right triangle opposite the right angle

reference triangle

used to solve inverse trig functions

tan (coordinate form)

vertical coordinate/horizontal coordinate

sin (coordinate form)

vertical coordinate/radius

standard position

when the initial point of a vector is at the origin