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