trig

Law of Sines

/sin(A) = b/sin(B) = c/sin(C); used to find missing sides or angles in non-right triangles (AAS or ASA). Must have a pair of angle and opposite side to start the proportion.

Law of Cosines

c^2 = a^2 + b^2 - 2ab cos(C); used to find a missing side with two sides and included angle (SAS), or angle with all three sides (SSS). Angle (C) must be between sides a and b.

Arc Length

s = r theta; used to find the length (s) of a section of a circle's circumference with radius (r). Angle (theta) must be in radians.

Standard Form of a Circle

(x - h)^2 + (y - k)^2 = r^2; defines a circle on a coordinate plane. Center coordinates (h, k) are always opposite in sign.

Quadratic Vertex

h = -b/2a; used to find the x-coordinate (h) of the vertex of a quadratic function. Watch the negative sign!

Logarithmic Conversion

log_b(y) = x longleftrightarrow b^x = y; converts between logarithmic and exponential form. The argument (y) must be > 0.

Volume of Similar Figures

VB/VA = k^3; finds the ratio of volumes for similar figures. Volume ratio is the cube of the linear ratio.

Distance Formula

d = sqrt((x2 - x1)^2 + (y2 - y1)^2); calculates distance between two points (x1, y1) and (x2, y2) on a coordinate plane.