1. 11. Solving Trig Equations

2. We’ll do the same things today as yesterday but today instead of x as the variable, we’ll have trig functions as the variable

3. Example: Solve for the variable.

4. Always look for a GCF first!

5. Difference of Squares

7. Factoring Trinomials

8. 3tan2 x– 14tanx + 8 1) Multiply 3 • (8) = 24; tanx2- 14tanx + 24
2) Set up ( )
( tanx )( tanx ) 3 3
What multiplies to 24 and adds to -14?
( tanx - 12)( tanx - 2) 3
4) Simplify (if possible).
5) Move denominator(s)in front of “x”.
( tanx - 4)( 3tanx - 2)

9. 2sec2 x– 3secx – 9 1) Multiply 2 • (-9) = -18; secx2 – 3secx - 18
2) Set up ( )
( secx )( secx ) 2 2
What multiplies to -18 and adds to -3?
( secx - 6)( secx + 3) 2
4) Simplify (if possible).
5) Move denominator(s)in front of “x”.
( secx - 3)( 2secx + 3)

10. 6sin3x + 13sin2x + 6sinx 1) Factor GCF sinx(6sin2x + 13sinx + 6)
2) Multiply 6 • (6) = 36;
Sinx(sin2x + 13sinx + 36)
3) Set up ( )
sinx( sinx )( sinx ) 6 6
4) What multiplies to 36 and adds to 13?
sinx(sin x + 4)( sinx + 9) 6
5) Simplify (if possible).
5) Move denominator(s)in front of “x”.
sinx(3sinx + 2)( 2sinx + 3)

11. Practice before finishing the rest of the notes!!

12. To finish solving Trig Equations
Solve the equation like normal, then look on unit circle to find angle

13. Notations for answers
If the problem says “find solutions between or “, then you will have a specific answer (or 2)
If the problem says “find ALL solutions”, add 360n OR 2πn to every answer

14. INVERSE TRIG. RESTRICTIONS
Remember to use inverse trig restrictions!!
Sin, csc, tan, cot are in the 1st and 4th quadrants
Cos and sec are in the 1st and 2nd quadrants

15. HELPFUL HINTS

16. Example
Find all solutions in degrees

17. Example
Find all solutions in radians

18. Example
Find all solutions in degrees

19. Example
Find solutions in