Pre-Calculus/Trig3+
Pre-Calculus/Trig3+ Name
5.3 Solving Trigonometric Equations Block Date
Review:
1. x2 – 4x + 3 = 0 2. x2 – 5x = 0 3. x = –[pic]+ 2
While some identities are true everywhere, others are only true at certain values. Today we are going to find those values. Well at least the values between 0o and 360o.
Steps to Solve a Trigonometric Equation:
1.
****** ONLY ALLOWED TO HAVE ONE TRIG FUNCTION IN EQUATION******
Note: Check your answer for false roots (especially when you square both sides or have a fraction)
2.
3.
4.
Examples:
1. 2 sin2[pic] - sin[pic] = 0 2. tan2[pic] - 2tan[pic] = 0
3. sin2[pic] - cos2[pic] - sin[pic] = 0 4. cos[pic] = 1 + 2sec[pic]
Pre-Calculus/Trig3 Name
5.3 Trig Equations Wkst Block Date
Solve for the principal values of [pic].
|1. 2cos[pic] + 1 = 0 |16. sin[pic] + 2csc[pic] = 3 |
|2. 5 sin[pic] - 1 = 0 |17. tan2[pic] - 3 = 0 |
|3. tan2 – 16 = 0 |18. 2cos2[pic] + sin[pic] - 1 = 0 |
|4. 2cos2[pic] - 3cos[pic] + 1 = 0 |19. 2sin2[pic] - 3sin[pic] + 1 = 0 |
|5. 8sin2[pic] - 2sin[pic] - 1 = 0 |20. 2cos[pic]sin[pic] = cos[pic] |
|6. 3tan4[pic] - 10tan2[pic] + 3 = 0 |21. 2cos(2[pic]) = ½ |
|7. tan2[pic] + 5tan[pic] + 6 = 0 |22. 2sin (½[pic]) + 1 = 0 |
|8. csc2[pic] - 6csc[pic] = 0 |23. tan2[pic]sin[pic] = - sin[pic] |
|9. sec2[pic] + sec[pic] - 2 = 0 |24. 2cos[pic]sin(2[pic]) = cos[pic] |
|10. 4cos4[pic] - 5cos2[pic] +1 = 0 |25. sin[pic] + sin[pic]cot[pic] = 0 |
|11. cos[pic] = 1 + 2sec[pic] |26. sec[pic] + cos[pic] = tan[pic]sin[pic] - 1 |
|12. sin[pic] - cos2[pic]sin[pic] = - 1 |27. tan2[pic] - sec[pic] = 1 |
|13. sec[pic] = sin2[pic]sec[pic] |28. 4cos[pic] - sec[pic] - 3 = 0 |
|14. sin2[pic] - tan[pic]cos2[pic] = 0 |29. 4 sin2(2[pic]) – 1 = 0 |
|15. 2sin[pic] - 3csc[pic] +5 = 0 |30. 2cos2(2[pic]) – cos(2[pic]) = 0 |
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