- altitude
- a perpendicular line from one vertex of a triangle to the opposite side, or in the case of an obtuse triangle, to the line containing 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$\text{\hspace{0.17em}}r=\theta .\text{\hspace{0.17em}}$When multiplied by a constant, the equation appears as$\text{\hspace{0.17em}}r=a\theta .\text{\hspace{0.17em}}$As$\text{\hspace{0.17em}}r=\theta ,\text{\hspace{0.17em}}$the curve continues to widen in a spiral path over the domain.

- 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 member of the limaçon family of curves, named for its resemblance to a heart; its equation is given as$\text{\hspace{0.17em}}r=a\pm b\mathrm{cos}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ and$\text{\hspace{0.17em}}r=a\pm b\mathrm{sin}\text{\hspace{0.17em}}\theta ,\text{\hspace{0.17em}}$where$\text{\hspace{0.17em}}\frac{a}{b}=1$

- convex limaҫon
- a type of one-loop limaçon represented by$\text{\hspace{0.17em}}r=a\pm b\mathrm{cos}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$and$\text{\hspace{0.17em}}r=a\pm b\mathrm{sin}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$such that$\text{\hspace{0.17em}}\frac{a}{b}\ge 2$

- De Moivre’s Theorem
- formula used to find the$\text{\hspace{0.17em}}n\text{th}\text{\hspace{0.17em}}$power or
*n*th roots of a complex number; states that, for a positive integer$\text{\hspace{0.17em}}n,{z}^{n}\text{\hspace{0.17em}}$is found by raising the modulus to the$\text{\hspace{0.17em}}n\text{th}\text{\hspace{0.17em}}$power and multiplying the angles by$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$

- dimpled limaҫon
- a type of one-loop limaçon represented by$\text{\hspace{0.17em}}r=a\pm b\mathrm{cos}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ and$\text{\hspace{0.17em}}r=a\pm b\mathrm{sin}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ such that$\text{\hspace{0.17em}}1<\frac{a}{b}<2$

- dot product
- given two vectors, the sum of the product of the horizontal components and the product of the vertical components

- Generalized Pythagorean Theorem
- an extension of the Law of Cosines; relates the sides of an oblique triangle and is used for SAS and SSS triangles

- initial point
- the origin of a vector

- inner-loop limaçon
- a polar curve similar to the cardioid, but with an inner loop; passes through the pole twice; represented by$\text{\hspace{0.17em}}r=a\pm b\mathrm{cos}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ and$\text{}r=a\pm b\mathrm{sin}\text{\hspace{0.17em}}\theta \text{}$where$\text{\hspace{0.17em}}a<b$

- Law of Cosines
- states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the included angle

- Law of Sines
- states that the ratio of the measurement of one angle of a triangle to the length of its opposite side is equal to the remaining two ratios of angle measure to opposite side; any pair of proportions may be used to solve for a missing angle or side

- lemniscate
- a polar curve resembling a figure 8 and given by the equation$\text{\hspace{0.17em}}{r}^{2}={a}^{2}\mathrm{cos}\text{\hspace{0.17em}}2\theta \text{\hspace{0.17em}}$and$\text{\hspace{0.17em}}{r}^{2}={a}^{2}\mathrm{sin}\text{\hspace{0.17em}}2\theta ,\text{\hspace{0.17em}}\text{\hspace{0.17em}}a\ne 0$

- magnitude
- the length of a vector; may represent a quantity such as speed, and is calculated using the Pythagorean Theorem

- modulus
- the absolute value of a complex number, or the distance from the origin to the point$\text{\hspace{0.17em}}\left(x,y\right);\text{\hspace{0.17em}}$also called the amplitude

- oblique triangle
- any triangle that is not a right triangle

- one-loop limaҫon
- a polar curve represented by$\text{\hspace{0.17em}}r=a\pm b\mathrm{cos}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ and$\text{\hspace{0.17em}}r=a\pm b\mathrm{sin}\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$ such that $a>0,b>0,$and$\text{\hspace{0.17em}}\frac{a}{b}>1;$ may be dimpled or convex; does not pass through the pole

- parameter
- a variable, often representing time, upon which$\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$and$\text{\hspace{0.17em}}y\text{\hspace{0.17em}}$are both dependent

- polar axis
- on the polar grid, the equivalent of the positive
*x-*axis on the rectangular grid

- polar coordinates
- on the polar grid, the coordinates of a point labeled$\text{\hspace{0.17em}}\left(r,\theta \right),\text{\hspace{0.17em}}$where$\text{\hspace{0.17em}}\theta \text{\hspace{0.17em}}$indicates the angle of rotation from the polar axis and$\text{\hspace{0.17em}}r\text{\hspace{0.17em}}$represents the radius, or the distance of the point from the pole in the direction of$\text{\hspace{0.17em}}\theta $

- polar equation
- an equation describing a curve on the polar grid.

- polar form of a complex number
- a complex number expressed in terms of an angle $\theta $ and its distance from the origin$\text{\hspace{0.17em}}r;\text{\hspace{0.17em}}$can be found by using conversion formulas$\text{\hspace{0.17em}}x=r\mathrm{cos}\text{\hspace{0.17em}}\theta ,\text{\hspace{0.17em}}\text{\hspace{0.17em}}y=r\mathrm{sin}\text{\hspace{0.17em}}\theta ,\text{\hspace{0.17em}}\text{\hspace{0.17em}}$and$\text{\hspace{0.17em}}r=\sqrt{{x}^{2}+{y}^{2}}$

- pole
- the origin of the polar grid

- resultant
- a vector that results from addition or subtraction of two vectors, or from scalar multiplication

- rose curve
- a polar equation resembling a flower, given by the equations$\text{\hspace{0.17em}}r=a\mathrm{cos}\text{\hspace{0.17em}}n\theta \text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}r=a\mathrm{sin}\text{\hspace{0.17em}}n\theta ;\text{\hspace{0.17em}}$when $\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$ is even there are $\text{\hspace{0.17em}}2n\text{\hspace{0.17em}}$ petals, and the curve is highly symmetrical; when$\text{\hspace{0.17em}}n\text{\hspace{0.17em}}$is odd there are $n$ petals.

- scalar
- a quantity associated with magnitude but not direction; a constant

- scalar multiplication
- the product of a constant and each component of a vector

- standard position
- the placement of a vector with the initial point at$\text{\hspace{0.17em}}\left(0,0\right)\text{\hspace{0.17em}}$and the terminal point$\text{\hspace{0.17em}}(a,b),\text{\hspace{0.17em}}$represented by the change in the
*x*-coordinates and the change in the*y*-coordinates of the original vector

- terminal point
- the end point of a vector, usually represented by an arrow indicating its direction

- unit vector
- a vector that begins at the origin and has magnitude of 1; the horizontal unit vector runs along the
*x*-axis and is defined as$\text{\hspace{0.17em}}{v}_{1}=\langle 1,0\rangle \text{\hspace{0.17em}}$the vertical unit vector runs along the*y*-axis and is defined as$\text{\hspace{0.17em}}{v}_{2}=\langle 0,1\rangle .$

- vector
- a quantity associated with both magnitude and direction, represented as a directed line segment with a starting point (initial point) and an end point (terminal point)

- vector addition
- the sum of two vectors, found by adding corresponding components