Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Trigonometry - Solving equations.
Test Yourself 2 - Solutions.


 

The questions below focus on the formats:
1. Trig ratio and a constant
2. Squared trig ratio and a constant.
3. Sin and cos terms but no constant.
4. Trig ratios in a quadratic format.
5. Using angles of any magnitude.
6. Number of solutions.

 

1. Trig ratio and a constant.

(solve all equations for
0 ≤ angle ≤ 360°).

 1. 2.
3. 4.
  5. 6.
  7. 8.
  9. . 10.
2. Squared trig ratio and a constant. 11.  
  13.  
  15.  
3. Sin and cos terms but no constant. 17. 18.
  19. 20.
  21.  
4. Trig ratios in a quadratic format. 23.  
  25. Solve 2cos2 x -3 cos x + 1 = 0
Answer.0°, 60°, 300°, 360°.		 26. Solve 3tan4 x + 2tan2 x - 1 = 0
Answer.30°, 150°, 210°, 330°.
  27. 3 sec2 x - tanx - 5 = 0
Answer.45°, 146°19', 225°, 326°19'.		 28. 2cot2x - cosecx + 1 = 0
Answer.90°.
  29. 30. (i)

(ii)

5. Complementary or supplementary angles.

(0 ≤ θ ≤ 360°).

 31. sinx = cos(2x - 45°).
Answer.45°.		 32. cos 3x = sin (x - 22°).
Answer.56°.
    34
6. Number of solutions. 35. 36