Interactive Trigonometry: Learn by Doing

Learning the two systems for measuring angles: degrees and radians.  Learning to convert between the two systems.

Learning about coterminal angles and reference angles.

Finding the arc length of a circle.  Finding the area of a sector.  Working with angular speed.

Learning to use the six basic trig functions: sin, cos, tan, csc, sec, cot.

There are a number of special values of the trig ratios which will be essential moving forward.  We will also look at the idea of cofunction identities.

Using trig functions to solve applied problems.

Introduction to the Unit Circle, which will be a central idea in the remainder of the course.

Defining the Pythagorean Identity.  Looking at the special trig ratios: 30, 45, and 60 degrees.

Using reference angles to complete the unit circle.

Finding exact values of the "other" trig functions: tangent, cosecant, secant, and cotangent.

Using even/odd identities and reciprocal identities.

Alternative forms of the Pythagorean Identity.  Finding exact values of the trig functions.

Graphing sine and cosine as functions.

Transformations of the sine and cosine functions.

Learning to graph the tangent function.

Learning to graph the remaining trig functions: Csc, Sec, Cot.

Working with the inverse sine, cosine, and tangent functions.

Working with composites of the trig functions which involve inverse functions.

Working with inverse functions involving algebraic expressions.

Verifying trig identities using substitution.

Using even/odd identities.  Using algebra to prove identities.

Using sum or difference formulas.

Sum or difference formula for tangent.  Using the sum or difference formulas in identities.

Using the double-angle formulas.

Using the power-reducing formulas.

Using the half-angle formulas.

Using product to sum formulas.

Using sum to product formulas.

Solving trig equations involving sine and cosine.

Solving trig equations involving double angles.

Solving trig equations involving quadratics.

Introduction to the Law of Sines.

Side, Side, Angle triangles and the Law of Sines.

Using the Law of Cosines on obtuse triangles without a complete ratio.

Solving applied problems involving the Law of Cosines.

Working in polar coordinates.  Converting between polar and rectangular coordinates.

Transforming equations between the rectangular and polar systems.

Transforming equations between polar and rectangular forms.

Working with the polar form of complex numbers.

Finding products, quotients, and powers of complex numbers in polar form.

Finding roots of complex numbers in polar form.

Introduction to vectors.

Addition, subtraction, and scalar multiplication with vectors.  Finding unit vectors.

Finding dot products of vectors.  Finding the angle between vectors.