High School Trigonometry Course

Time4Learning offers an online, interactive high school curriculum that correlates to state standards. It can be used as a primary homeschool curriculum, a supplement to your current curriculum and as an afterschool or summer skill building program. At the high school level, Time4Learning is organized by courses rather than grade levels, so parents have the option of choosing any four as part of membership.

The Trigonometry curriculum is one of five Math courses offered at the high school level. Trigonometry is taught using a combination of multimedia lessons, instructional videos, worksheets, quizzes, tests and both online and offline projects. The Trigonometry course is designed to prepare students for college level mathematics.

This page includes information about the material covered in the High School Trigonometry course.

Chapter 1 – Trigonometry and Triangles

The materials in this chapter introduce and cover the basics of trigonometry and triangles. It is organized into sections that teach, reinforce and test students on the concepts of right-triangle trigonometry and solving triangles.

Lessons in this chapter are organized into the following sections:

  • Right-triangle trigonometry – Students learn how to measure right triangles using right-angle trigonometry.
  • Solving triangles – Students are taught how to measure triangles following the Laws of Sines and the Law of Cosines. Area is taught next using Heron’s Formula.

Chapter 2 – The Unit Circle

The materials in this chapter introduce and cover the the unit circle. It is organized into sections that teach, reinforce and test students on the concepts of right-angle relationships in the unit circle, angles in the unit circle and periodic functions.

Lessons in this chapter are organized into the following sections:

  • Right-angle relationships in the unit circle – Students learn how to use right-angle relationships to define trigonometric functions in the unit circle.
  • Angles in the unit circle – Students are taught how to locate angles of rotation and reference angles, and how to convert from degrees to radians and vice versa.
  • Periodic functions – Students are required to evaluate the trigonometric functions of any angle in degrees or radians and find the relationship of the graphs of sine and cosine to the unit circle. Students must then find the period of trigonometric functions in order to conclude whether a trigonometric function is even or odd.

Chapter 3 – Trigonometric Functions

The materials in this chapter introduce and cover trigonometric functions. It is organized into sections that teach, reinforce and test students on the concepts of trigonometric functions, transformations, reciprocal functions and inverse trigonometric functions.

Lessons in this chapter are organized into the following sections:

  • Trigonometric functions – Students are required to learn the difference between sine, cosine and tangent, and how to graph them.
  • Transformations – Students are taught the rules for vertical and horizontal translations and then how to use them, along with stretches and compressions, to transform trigonometric functions.
  • Reciprocal functions – Students learn the differences between cosecant, secant and contangent functions and how to graph them.
  • Inverse trigonometric functions – Students are required to define, evaluate and recognize graphs of inverse trigonometric functions.

Chapter 4 – Trigonometric Equations

The materials in this chapter introduce and cover trigonometric equations. It is organized into sections that teach, reinforce and test students on the concepts of trigonometric identities and solving trigonometric equations.

Lessons in this chapter are organized into the following sections:

  • Trigonometric identities – Students are required to use trigonometric identities, such as Pythagorean identity, the sum, difference, double-angle and half-angle identities.
  • Solving trigonometric equations – Students will learn how to solve trigonometric equations by using inverse trigonometric functions, substitution, and trigonometric identities.

Chapter 5 – Vectors

The materials in this chapter introduce and cover vectors. It is organized into sections that teach, reinforce and test students on the concepts of forms of vectors and vector operations.

Lessons in this chapter are organized into the following sections:

  • Forms of vectors – Students learn how to write and use vectors in component form.
  • Vector operations – Students are required to add, subtract and multiply vectors, including using using scalar multiplication, dot products, and the cross products of vectors. The lesson concludes by teaching students how to use the Pythagorean Theorem and right triangle trigonometry to solve vector application problems.

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