trig vocab

cycle

a permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion

equation of a circle:(x-h)² + (y-k)² = r²

If the center of the circle is at the origin of the coordinate plane, the equation is where r is the radius. When the center of the circle is at the point (h,k), the equation becomes

cirlce

a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)

center

a point inside the circle and is at an equal distance from all of the points on its circumference. The constant distance from the center of the circle to any point on the circle is called the radius of the circle.

converting from radians to degrees

The general formula for converting from radians to degrees to simply multiply the number of degree by 180°/(Π)

theta

a Greek symbol used in math. It does not have a specific meaning. Its meaning is often defined by its usage or context.

periodic function math

a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of 2π radians.

chord to a circle

a line segment drawn from any point on the circumference of the circle to any other point on the circumference of the circle.

secant line to a circle

a line segment which passes through a circle. Since the secant is a straight line and circle is a curve, a secant intersects the circle only at two points.

tangent line to a circle

a line that touches the circle at exactly one point, never entering the circle's interior.

sine

a trigonometric function of an angle. the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle (that is not the hypotenuse) to the length of the longest side of the triangle (the hypotenuse).

radian

a unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius.

negative angle in standard position

an angle is drawn in what is called the "standard position". The vertex of the angle is on the origin, and one side of the angle is fixed and drawn along the positive x-axis

central angle

an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. The central angle is subtended by an arc between those two points, and the arc length is the central angle (measured in radians) times the radius.

major arc

an arc of a circle having measure greater than or equal to ( radians).

conterminal angles

angles in coordinate plane that result out of rotation of the terminal side of angles in standard position.

diameter

any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle.

converting from degrees to radians

convert from degrees to radians, multiply by π/180

period

if all real numerical values of x, the numerical values of a function at (t + b) is same as the number of function at x, that is f(t+b) = f(t) then we can call the function is periodic and the period is 'b'.

quadrantal angle

if its terminal side lies on x-axis or y-axis. Quadrantal angles include 0∘, ±90∘, ±180∘, ±270∘, ±360∘ etc.

the unit circle

is a circle, centered at the origin, with a radius of 1.

45-45-90 triangle relationship

isosceles right triangle is a triangle with angles of 45°, 45°, and 90°

positive angle in standard position

its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

minor arc

smaller of the two arcs formed when a circle is divided into two unequal parts. The measure of the minor arc is always less than 180° or π radian. The sum of the measures of the major arc and the minor arc is equal to 360° or 2π radian

30-60-90 triangle relationship

special right triangle (a right triangle being any triangle that contains a 90 degree angle) that always has degree angles of 30 degrees, 60 degrees. it also has side length values which are always in a consistent relationship with one another.

inscribed angle

the angle formed in the interior of a circle when two secant lines (or, in a degenerate case, when one secant line and one tangent line of that circle) intersect on the circle.

amplitude

the height from the mean, or rest, value of the function to its maximum or minimum. The period is the distance required for the function to complete one full cycle.

radius

the length of a line segment from its center to its perimeter.

arc length in radians

the measure of the distance along the curved line making up the arc. It is longer than the straight line distance between its endpoints

cosine

the trigonometric function that is equal to the ratio of the side adjacent to an acute angle to the hypotenuse.

tangent

the trigonometric function that is equal to the ratio of the sides (other than the hypotenuse) opposite and adjacent to an angle in a right triangle.

point of tangency

which a line touches an ellipse or circle, assuming that the line only makes contact at one point. The line running through the point of tangency only has that one point in common with the circle or ellipse, and it is called a "tangential" line with respect to that shape.