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Done By: Loo Nathanael (18) Chen Jiun Wei (4) Goh Xian Fong (12) Yap Jian Shern (24)

Trigonometric Equations. Done By: Loo Nathanael (18) Chen Jiun Wei (4) Goh Xian Fong (12) Yap Jian Shern (24). Agenda. Introduction Solving trigonometric equations Solving for Oblique triangles Revision. Solving Trigonometric Equations. Many methods to solve

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Done By: Loo Nathanael (18) Chen Jiun Wei (4) Goh Xian Fong (12) Yap Jian Shern (24)

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  1. Trigonometric Equations Done By: Loo Nathanael (18) Chen Jiun Wei (4) Goh Xian Fong (12) Yap Jian Shern (24)

  2. Agenda • Introduction • Solving trigonometric equations • Solving for Oblique triangles • Revision

  3. Solving Trigonometric Equations • Many methods to solve • Related to solving algebraic equations • Quite easy to handle • TAKE NOTE: Numbers pertaining to angles must be written with the degree sign

  4. Trigonometric Identities

  5. Example 2 sinX – 1 = 0 ???

  6. Method • Move the number over to the other end • Remove the coefficient of the sin X • Arcsine the fraction to get X • In this case, special-angle rules apply • Most commonly used method

  7. Method

  8. Example 2 sin x – cos x = 0

  9. Method

  10. Checking for Answers • Numerical Check • Substitute the answer into the equations and see whether both sides of the equation are balanced • Graphical Check • Write the equation, eg. f(x) = 2 sinX – 1 • The line will intercept the x-axis many times • Check if one of these intercepts is your answer

  11. How to use the Identities • Conversion of functions • From tan to sin and cos • From sin and cos to tan • From sin2 to cos2 • From cos2 to sin2 • Most commonly used identities

  12. Solving for Scalene Triangles • TAKE NOTE: Special-angle rules learned previously are different in these questions and do not apply here • Useful in deriving lengths or angles of scalene triangles instead of subtracting one angle from another • Trigonometric formulae must be used here

  13. Types of Questions • 4 sets of unknowns: (one of them must be revealed) • Two sides and an angle opposite to one of them • Two angles and any side • Two sides and the included angle • All three sides

  14. Types (1) and (2)

  15. Example- Types (1) and (2) B c a A C b

  16. Method – Types (1) and (2)

  17. Method – Types (1) and (2)

  18. Method – Types (1) and (2)

  19. Types (3) and (4)

  20. Example - Types (3) and (4) Solve triangle ABC if a=5, b=6 and c=9. C b a A B c

  21. Method- Types (3) and (4)

  22. Method- Types (3) and (4) • Then, use the law of sines to find out the values of angles A and B. • You will eventually be able to solve the triangle.

  23. Questions?

  24. worksheet time…..

  25. Thank you! We hope you had an Enjoyable lesson!

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