Unit 8

altitude

A perpendicular line from one vertex of a triangle to the opposite side, forming two right triangles.

ambiguous case

A scenario in which more than one triangle is a valid solution for a given oblique SSA triangle.

Archimedes’ spiral

A polar curve given by r=θ that widens in a spiral path.

argument

The angle associated with a complex number; the angle between the line from the origin to the point and the positive real axis.

cardioid

A curve resembling a heart, represented by r=a±bcosθ or r=a±bsinθ.

convex limaçon

A one-loop limaçon represented by r=a±bcosθ and r=a±bsinθ such that ab≥2.

De Moivre’s Theorem

A formula to find the nth power or nth roots of a complex number.

dot product

The sum of the product of the horizontal components and the product of the vertical components of two vectors.

Law of Sines

States the ratio of the angles of a triangle to the lengths of its opposite sides.

Law of Cosines

Relates the lengths of the sides of a triangle to the cosine of one of its angles.

Heron’s formula

Area of a triangle calculated with all three sides known.

polar coordinates

Coordinates of a point in the form (r,θ) in the polar grid.

polar equation

An equation describing a curve on the polar grid.

resultant

A vector resulting from the addition or subtraction of two vectors.

rose curve

A polar equation resembling a flower given by r=acosnθ or r=asinnθ.

scalar multiplication

The product of a constant and each component of a vector.

unit vector

A vector that begins at the origin and has a magnitude of 1.

vector

A quantity associated with both magnitude and direction.