Introduction to Trigonometry


This final chapter introduces you to trigonometry and provides a foundation for higher-level courses. After covering the basic trigonometric ratios, their inverses, and applications to real-world problems and areas, vectors and reciprocal ratios are covered. The chapter concludes with derivations and applications of the Law of Cosines and Law of Sines.

What you can expect to learn

After completing these activities you should be able to

  1. Define the three basic trigonometric ratios and the three reciprocal ratios.
  2. Evaluate trigonometric ratios, including exact values for 30º, 45º, and 60º angles.
  3. Solve right triangles using trigonometric ratios.
  4. Apply trigonometry to calculate indirect measurements related to surveying and other applications.
  5. Calculate areas of triangles and regular polygons using trigonometric ratios.
  6. Express vectors in component form and by their magnitude and direction.
  7. Perform simple vector operations.
  8. Verify trigonometric identities.
  9. Apply the Law of Cosines and Law of Sines to solve oblique triangles.
Activity List