The Unit Circle: Angles, Coordinates and Trig Values
The unit circle explained: why the coordinates are cos and sin, every special angle in degrees and radians, tangent on the unit circle, and memory tricks.
Category: Precalculus
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Trigonometric Functions: Sin, Cos, Tan, Table and Graphs
The six trig functions with SOH-CAH-TOA and the unit circle, a table of exact values (sin 30, cos 180, sec 45), graphs, period and amplitude.
Trig Identities: Full List with Double Angle Formulas
Every trig identity you need: Pythagorean, reciprocal, sum and difference, double angle and half angle formulas, with proofs and worked examples.
Special Right Triangles: 45-45-90 and 30-60-90 Rules
The 45-45-90 and 30-60-90 special right triangles: side ratios, where they come from, how to find missing sides, exact trig values and practice problems.
Slope Formula: Point-Slope and Slope-Intercept Form
How to find the slope of a line from two points, a graph or an equation, plus point-slope and slope-intercept form, parallel and perpendicular lines.
Quadratic Formula: Derivation, Discriminant, Examples
How to use the quadratic formula, where it comes from, what the discriminant tells you, how to find the vertex of a parabola, plus practice problems.
Polynomials: Definition, Degree, Zeros and Graphs Explained
What a polynomial is, degree and leading coefficient, finding zeros by factoring, the rational root test and synthetic division, and end behavior.
Matrix Multiplication, Determinant and Inverse Explained
How to multiply matrices (row times column), when it is possible, 2×2 and 3×3 determinants, the inverse matrix and solving systems.
Logarithm Rules: Log Properties, Change of Base, Graphs
All the log rules (product, quotient, power, change of base) with proofs, plus how to solve log and exponential equations and graph a log function.
Law of Sines and Law of Cosines: When to Use Each
The law of sines and law of cosines: formulas, how to choose (SSS, SAS, ASA, AAS, SSA), the ambiguous case, proofs, triangle area and examples.