Introduction to basic trigonometry functions and their properties.

• Trigonometry functions such as sine, cosine, and tangent are defined using right triangles and the unit circle.
• Special angles (30, 45, 60 degrees) and their sine and cosine values are calculated.
• The concepts of domain, range, periodicity, and symmetry for sine and cosine functions are explained.

Explanation of inverse trigonometry functions and their usage.

• Inverse trigonometry functions like arcsine, arccosine, and arctangent are introduced.
• The domain and range for each inverse function are provided.
• Examples of finding angles using inverse trigonometry functions are demonstrated.

Derivation and application of angle sum and double angle formulas.

• Angle sum formulas for sine and cosine are stated and proved geometrically.
• Double angle formulas for sine and cosine are derived and examples are provided.
• Use of these formulas to solve trigonometry problems is illustrated.

Introduction to half angle formulas and their practical use cases.

• Half angle formulas for sine and cosine are provided.
• A step-by-step guide on using these formulas to find sine and cosine of half angles.
• An example using the half angle formulas to find exact trigonometry values.

Techniques for solving right triangles using trigonometry.

• Methods for finding missing side lengths and angles in right triangles are covered.
• Use of trigonometric ratios and the Pythagorean Theorem in solving triangles is explained.
• Examples of solving right triangles with different given information.

Explanation of the Law of Cosines and its application to non-right triangles.

• The Law of Cosines is explained as a generalization of the Pythagorean Theorem.
• Examples demonstrate solving for sides and angles of non-right triangles using the Law of Cosines.
• Different forms of the Law of Cosines are presented based on the known elements of the triangle.

The Law of Sines is discussed with examples showing how to solve for unknown triangle measures.

• The Law of Sines is described for finding measures in any triangle.
• Examples showing the use of the Law of Sines to solve for angles and sides.
• The ambiguous case of SSA triangles is addressed with examples.

Overview of parametric equations and converting between coordinate systems.

• Parametric equations are introduced as a way to describe curves that fail the vertical line test.
• Conversion between parametric and Cartesian equations is explained with examples.
• Equations of circles are represented both parametrically and in Cartesian form.

Conic sections including parabolas and ellipses are explored with their equations.

• The definition and equation of a parabola are explained with focus and directrix.
• Ellipses are defined with their major and minor axes, vertices, and foci.
• Equations for parabolas and ellipses with shifted vertices are provided.

An introduction to hyperbolas, their features, and equations.

• Hyperbolas are defined as the set of points with a constant difference in distance from two foci.
• Vertices, center, and asymptotes of hyperbolas are discussed.
• Equations for hyperbolas with horizontal and vertical orientations are provided.