Trigonometry

Introduction

This chapter on trigonometry builds on the foundations that have been covered in Sec 2 Trigonometry and the Sec 3 Trigonometry covered in Elementary Mathematics.

Success Criteria

At the end of this chapter, students are able to:

1. 1. State the value of trigonometric ratios for Special Angles.

   2. Apply the complementary angle relationship.

   3. Use the Unit Circle to extend trigonometric functions to angles beyond 90°.

   4. Solve simple trigonometric equations for angles between 0° and 360°.

   5. Evaluate the trigonometric ratio of negative angles and angles beyond 360°.

   6. State the definition of the secant, cosecant and cotangent function.

   7. State the domain of principal values and range of values of P for which the inverse trigonometric ratio of P is defined.

   8. State the amplitude, period, axis-of-curve, maximum & minimum value for trigonometric equations of the forms: (i) AsinBx + C; (ii) AcosBx + C; and (iii) AtanBx + C.

   9. Sketch trigonometric graphs of the forms: (i) AsinBx + C; (ii) AcosBx + C; and (iii) AtanBx + C.

   10. Express tangent and cotangent as a fraction of sine and cosine.

   11. Apply the Pythagorean Identities.

   12. Prove trigonometric identities.

   13. Solve trigonometric equations.

   14. Apply the Double-Angle Formulas.