Analytic Trig, Applications, Polar and Vectors
You prove and use the trig identities, solve trig equations, apply trig to real triangles with the laws of sines and cosines, and finish with polar coordinates, complex numbers and vectors.
Class 1Trigonometric identities
The equations that are always true, and why they help.
Class 2Sum and difference formulas
The angle-adding formulas, and what they unlock.
Class 3Double-angle and half-angle formulas
Formulas for twice an angle and half an angle.
Class 4Product-to-sum and sum-to-product formulas
Turning products of trig functions into sums, and back.
Class 5Trigonometric equations
Finding the angles that make a trig equation true.
Class 6Right triangle applications
Solving real problems with a right triangle.
Class 7The law of sines
Solving triangles that are not right-angled.
Class 8The law of cosines and area
The other law for hard triangles, and finding area.
Class 9Polar coordinates
Locating a point by angle and distance.
Class 10Polar equations and graphs
The pretty curves polar equations draw.
Class 11Complex numbers in polar form
Writing and powering complex numbers with trig.
Class 12Vectors and the dot product
Quantities with size and direction, and how to combine them.