Trigonometric Equations (using identities) in given intervals – Further Maths

Last updated: 09/03/2020

AQA Level 2 Certificate in Further Maths Geometry Trigonometric Equations (using identities) in given intervals – Further Maths

Question 1 of 44

1. Question
“Solve ” cosθ/sinθ=-1.639″ between “-180°≤θ≤180°
- θ=-31.4°,148.6°
- θ=-62.8°,297.2°
- θ=-15.7°,74.3°
- θ=-47.1°,222.9°
Correct

Incorrect
Question 2 of 44

2. Question
“Solve ” cosθ/sinθ=-4.545″ between ” 0°≤θ≤360°
- θ=167.6°,347.6°
- θ=137.6°,317.6°
- θ=335.2°,695.2°
- θ=251.4°,521.4°
Correct

Incorrect
Question 3 of 44

3. Question
“Solve ” cosθ=2 1/2 sinθ” between ” 0°≤θ≤360°
- θ=21.8°,201.8°
- θ=14.5°,134.5°
- θ=-8.2°,171.8°
- θ=6.8°,186.8°
Correct

Incorrect
Question 4 of 44

4. Question
“Solve ” sinθ=4/5 cosθ” between “-180°≤θ≤180°
- θ=-141.3°,38.7°
- θ=-212.0°,58.0°
- θ=-126.3°,53.7°
- θ=-156.3°,23.7°
Correct

Incorrect
Question 5 of 44

5. Question
“Solve ” sinθ=-4/5 cosθ” between ” 0°≤θ≤360°
- θ=141.3°,321.3°
- θ=282.7°,642.7°
- θ=126.3°,306.3°
- θ=171.3°,351.3°
Correct

Incorrect
Question 6 of 44

6. Question
“Solve ” sinθ/cosθ=0.62″ between ” 0°≤θ≤360°
- θ=31.8°,211.8°
- θ=63.6°,423.6°
- θ=46.8°,226.8°
- θ=16.8°,196.8°
Correct

Incorrect
Question 7 of 44

7. Question
“Solve ” sinθ=9/10 cosθ” between ” 0°≤θ≤360°
- θ=42.0°,222.0°
- θ=21.0°,111.0°
- θ=72.0°,252.0°
- θ=57.0°,237.0°
Correct

Incorrect
Question 8 of 44

8. Question
“Solve ” cosθ=-1 1/9 sinθ” between “-180°≤θ≤180°θ=57.0°,237.0°
- θ=-42.0°,138.0°
- θ=-12.0°,168.0°
- θ=-27.0°,153.0°
- θ=-28.0°,92.0°
Correct

Incorrect
Question 9 of 44

9. Question
“Solve ” sinθ=-1cosθ” between “-180°≤θ≤180°
- θ=-45.0°,135.0°
- θ=-30.0°,150.0°
- θ=-30.0°,90.0°
- θ=-67.5°,202.5°
Correct

Incorrect
Question 10 of 44

10. Question
“Solve ” sinθ=-1cosθ” between “-180°≤θ≤180°
- θ=-45.0°,135.0°
- θ=-67.5°,202.5°
- θ=-30.0°,90.0°
- θ=-30.0°,150.0°
Correct

Incorrect
Question 11 of 44

11. Question
“Solve ” sinθ=-7/10 cosθ” between ” 0°≤θ≤360°
- θ=145.0°,325.0°
- θ=96.7°,216.7°
- θ=290.0°,650.0°
- θ=130.0°,310.0°
Correct

Incorrect
Question 12 of 44

12. Question
“Solve ” cosθ/sinθ=1.639″ between “-180°≤θ≤180°
- θ=-148.6°,31.4°
- θ=-99.1°,20.9°
- θ=-163.6°,16.4°
- θ=-74.3°,15.7°
Correct

Incorrect
Question 13 of 44

13. Question
“Solve ” sinθ/cosθ=-0.83″ between ” 0°≤θ≤360°
- θ=140.3°,320.3°
- θ=125.3°,305.3°
- θ=210.5°,480.5°
- θ=155.3°,335.3°
Correct

Incorrect
Question 14 of 44

14. Question
“Solve ” sinθ/cosθ=0.24″ between “-180°≤θ≤180°
- θ=-166.5°,13.5°
- θ=-181.5°,-1.5°
- θ=-136.5°,43.5°
- θ=-249.8°,20.2°
Correct

Incorrect
Question 15 of 44

15. Question
“Solve ” cosθ/sinθ=1.515″ between “-180°≤θ≤180°
- θ=-146.6°,33.4°
- θ=-116.6°,63.4°
- θ=-73.3°,16.7°
- θ=-161.6°,18.4°
Correct

Incorrect
Question 16 of 44

16. Question
Solve 12sin²θ + 8sinθ + 1 = 0: between 0° ≤ θ ≤ 360°
- θ = 189.6°, 210.0°, 330.0°, 350.4°
- θ = 126.4°, 140.0°, 220.0°, 233.6°
- θ = 284.4°, 315.0°, 495.0°, 525.6°
- θ = 94.8°, 105.0°, 165.0°, 175.2°
Correct

Incorrect
Question 17 of 44

17. Question
Solve 12sin²θ + 6 = 17sinθ: between -180° ≤ θ ≤ 180°
- θ = 41.8°, 48.6°, 131.4°, 138.2°
- θ = 56.8°, 63.6°, 146.4°, 153.2°
- θ = 27.9°, 32.4°, 87.6°, 92.1°
- θ = 11.8°, 18.6°, 101.4°, 108.2°
Correct

Incorrect
Question 18 of 44

18. Question
Solve 12sin²θ + sinθ = 6:between -180° ≤ θ ≤ 180°
- θ = -131.4°, -48.6°, 41.8°, 138.2°
- θ = -116.4°, -33.6°, 56.8°, 153.2°
- θ = -146.4°, -63.6°, 26.8°, 123.2°
- θ = -101.4°, -18.6°, 71.8°, 168.2°
Correct

Incorrect
Question 19 of 44

19. Question
Solve 12sin²θ = 5sinθ + 3: between 0° ≤ θ ≤ 360°
- θ = 48.6°, 131.4°, 199.5°, 340.5°
- θ = 18.6°, 101.4°, 169.5°, 310.5°
- θ = 24.3°, 65.7°, 99.7°, 170.3°
- θ = 32.4°, 87.6°, 133.0°, 227.0°
Correct

Incorrect
Question 20 of 44

20. Question
Solve 12sin²θ + sinθ = 1: between 0° ≤ θ ≤ 360°
- θ = 14.5°, 165.5°, 199.5°, 340.5°
- θ = -0.5°, 150.5°, 184.5°, 325.5°
- θ = -15.5°, 135.5°, 169.5°, 310.5°
- θ = 29.5°, 180.5°, 214.5°, 355.5°
Correct

Incorrect
Question 21 of 44

21. Question
Solve 8cos²θ = 2cosθ + 3: between -180° ≤ θ ≤ 180°
- θ = -120.0°, -41.4°, 41.4°, 120.0°
- θ = -60.0°, -20.7°, 20.7°, 60.0°
- θ = -105.0°, -26.4°, 56.4°, 135.0°
- θ = -150.0°, -71.4°, 11.4°, 90.0°
Correct

Incorrect
Question 22 of 44

22. Question
Solve 12cos²θ + 5cosθ = 2: between 0° ≤ θ ≤ 360°
- θ = 75.5°, 131.8°, 228.2°, 284.5°
- θ = 37.8°, 65.9°, 114.1°, 142.2°
- θ = 113.3°, 197.7°, 342.3°, 426.7°
- θ = 45.5°, 101.8°, 198.2°, 254.5°
Correct

Incorrect
Question 23 of 44

23. Question
Solve 14cos²θ + cosθ = 3: between 0° ≤ θ ≤ 360°
- θ = 64.6°, 120.0°, 240.0°, 295.4°
- θ = 32.3°, 60.0°, 120.0°, 147.7°
- θ = 129.2°, 240.0°, 480.0°, 590.8°
- θ = 49.6°, 105.0°, 225.0°, 280.4°
Correct

Incorrect
Question 24 of 44

24. Question
Solve 9cos²θ = 3cosθ + 2: between -180° ≤ θ ≤ 180°
- θ = -109.5°, -48.2°, 48.2°, 109.5°
- θ = -94.5°, -33.2°, 63.2°, 124.5°
- θ = -73.0°, -32.1°, 32.1°, 73.0°
- θ = -79.5°, -18.2°, 78.2°, 139.5°
Correct

Incorrect
Question 25 of 44

25. Question
Solve 12cos²θ + cosθ = 6: between 0° ≤ θ ≤ 360°
- θ = 48.2°, 138.6°, 221.4°, 311.8°
- θ = 72.3°, 207.9°, 332.1°, 467.7°
- θ = 18.2°, 108.6°, 191.4°, 281.8°
- θ = 33.2°, 123.6°, 206.4°, 296.8°
Correct

Incorrect
Question 26 of 44

26. Question
Solve 14tan²θ = 3tanθ + 5: between -180° ≤ θ ≤ 180°
- θ = -144.5°, -26.6°, 35.5°, 153.4°
- θ = -288.9°, -53.1°, 71.1°, 306.9°
- θ = -129.5°, -11.6°, 50.5°, 168.4°
- θ = -216.7°, -39.8°, 53.3°, 230.2°
Correct

Incorrect
Question 27 of 44

27. Question
Solve 15tan²θ + tanθ = 6: between 0° ≤ θ ≤ 360°
- θ = 31.0°, 146.3°, 211.0°, 326.3°
- θ = 61.9°, 292.6°, 421.9°, 652.6°
- θ = 46.4°, 219.5°, 316.4°, 489.5°
- θ = 61.0°, 176.3°, 241.0°, 356.3°
Correct

Incorrect
Question 28 of 44

28. Question
Solve 9tan²θ + 2 = 9tanθ: between 0° ≤ θ ≤ 360°
- θ = 18.4°, 33.7°, 198.4°, 213.7°
- θ = 33.4°, 48.7°, 213.4°, 228.7°
- θ = -11.6°, 3.7°, 168.4°, 183.7°
- θ = 12.3°, 22.5°, 132.3°, 142.5°
Correct

Incorrect
Question 29 of 44

29. Question
Solve 12tan²θ + tanθ = 1: between 0° ≤ θ ≤ 360°
- θ = 14.0°, 161.6°, 194.0°, 341.6°
- θ = 7.0°, 80.8°, 97.0°, 170.8°
- θ = 44.0°, 191.6°, 224.0°, 371.6°
- θ = 29.0°, 176.6°, 209.0°, 356.6°
Correct

Incorrect
Question 30 of 44

30. Question
Solve 12tan²θ + 4tanθ = 5: between 0° ≤ θ ≤ 360°
- θ = 26.6°, 140.2°, 206.6°, 320.2°
- θ = 11.6°, 125.2°, 191.6°, 305.2°
- θ = 39.8°, 210.3°, 309.8°, 480.3°
- θ = 41.6°, 155.2°, 221.6°, 335.2°
Correct

Incorrect
Question 31 of 44

31. Question
“Solve ” (tanθ+tan2θ)/(1+tanθtan2θ)=-0.24″ between ” 0°≤θ≤360°
- θ=55.5°,115.5°,175.5°,235.5°,295.5°,355.5°
- θ=37.0°,77.0°,117.0°,157.0°,197.0°,237.0°
- θ=83.3°,173.3°,263.3°,353.3°,443.3°,533.3°
- θ=27.8°,57.8°,87.8°,117.8°,147.8°,177.8°
Correct

Incorrect
Question 32 of 44

32. Question
Solve cosθcos2θ-sinθsin2θ=0.92″ between “-180°≤θ≤180°
- θ=-127.7°,-112.3°,-7.7°,7.7°,112.3°,127.7°
- θ=-63.8°,-56.2°,-3.8°,3.8°,56.2°,63.8°
- θ=-97.7°,-82.3°,22.3°,37.7°,142.3°,157.7°
- θ=-157.7°,-142.3°,-37.7°,-22.3°,82.3°,97.7°
Correct

Incorrect
Question 33 of 44

33. Question
“Solve ” (tanθ-tan2θ)/(1-tanθtan2θ)=-0.97″ between ” 0°≤θ≤360°
- θ=44.1°,224.1°
- θ=22.1°,112.1°
- θ=88.3°,448.3°
- θ=29.1°,209.1°
Correct

Incorrect
Question 34 of 44

34. Question
“Solve ” sin3θcosθ-cos3θsinθ=-0.51″ between “-180°≤θ≤180°
- θ=-74.7°,-15.3°,105.3°,164.7°
- θ=-149.3°,-30.7°,210.7°,329.3°
- θ=-104.7°,-45.3°,75.3°,134.7°
- θ=-49.8°,-10.2°,70.2°,109.8°
Correct

Incorrect
Question 35 of 44

35. Question
“Solve ” (tanθ-tan2θ)/(1-tanθtan2θ)=0.69″ between “-180°≤θ≤180°
- θ=-34.6°,145.4°
- θ=-23.1°,96.9°
- θ=-69.2°,290.8°
- θ=-17.3°,72.7°
Correct

Incorrect
Question 36 of 44

36. Question
“Solve ” sin2θcosθ-cos2θsinθ=0.96″ between ” 0°≤θ≤360°
- θ=73.7°,106.3°
- θ=43.7°,76.3°
- θ=49.2°,70.8°
- θ=147.5°,212.5°
Correct

Incorrect
Question 37 of 44

37. Question
“Solve ” cosθcos2θ+sinθsin2θ=-0.73″ between “-180°≤θ≤180
- θ=-136.9°,136.9°
- θ=-166.9°,106.9°
- θ=-273.8°,273.8°
- θ=-91.3°,91.3°
Correct

Incorrect
Question 38 of 44

38. Question
“Solve ” sinθcos2θ+cosθsin2θ=-0.79″ between ” 0°≤θ≤360°
- θ=77.4°,102.6°,197.4°,222.6°,317.4°,342.6°
- θ=154.8°,205.2°,394.8°,445.2°,634.8°,685.2°
- θ=51.6°,68.4°,131.6°,148.4°,211.6°,228.4°
- θ=107.4°,132.6°,227.4°,252.6°,347.4°,372.6°
Correct

Incorrect

<math xmlns=”http://www.w3.org/1998/Math/MathML”><mtext>Solve </mtext><mi>s</mi><mi>i</mi><mi>n</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>c</mi><mi>o</mi><mi>s</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>+</mo><mi>c</mi><mi>o</mi><mi>s</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>s</mi><mi>i</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>=</mo><mo>−</mo><mn>0.09</mn><mspace linebreak=”newline” /><mtext> between </mtext><mo>−</mo><mn>180</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow><mo>≤</mo><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>≤</mo><mn>180</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow></math>

$θ = - 178.3 °, - 121.7 °, - 58.3 °, - 1.7 °, 61.7 °, 118.3 °$
$θ = - 208.3 °, - 151.7 °, - 88.3 °, - 31.7 °, 31.7 °, 88.3 °$
$θ = - 118.9 °, - 81.1 °, - 38.9 °, - 1.1 °, 41.1 °, 78.9 °$
$θ = - 89.1 °, - 60.9 °, - 29.1 °, - 0.9 °, 30.9 °, 59.1 °$

<math xmlns=”http://www.w3.org/1998/Math/MathML”><mtext>Solve </mtext><mi>c</mi><mi>o</mi><mi>s</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>c</mi><mi>o</mi><mi>s</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>−</mo><mi>s</mi><mi>i</mi><mi>n</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>s</mi><mi>i</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>=</mo><mn>0.52</mn><mspace linebreak=”newline” /><mtext> between </mtext><mo>−</mo><mn>180</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow><mo>≤</mo><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>≤</mo><mn>180</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow></math>

$θ = - 139.6 °, - 100.4 °, - 19.6 °, 19.6 °, 100.4 °, 139.6 °$
$θ = - 279.1 °, - 200.9 °, - 39.1 °, 39.1 °, 200.9 °, 279.1 °$
$θ = - 169.6 °, - 130.4 °, - 49.6 °, - 10.4 °, 70.4 °, 109.6 °$
$θ = - 93.0 °, - 67.0 °, - 13.0 °, 13.0 °, 67.0 °, 93.0 °$

<math xmlns=”http://www.w3.org/1998/Math/MathML”><mtext>Solve </mtext><mrow class=”MJX-TeXAtom-ORD”><mfrac><mrow class=”MJX-TeXAtom-ORD”><mi>t</mi><mi>a</mi><mi>n</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>+</mo><mi>t</mi><mi>a</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow></mrow><mrow class=”MJX-TeXAtom-ORD”><mn>1</mn><mo>+</mo><mi>t</mi><mi>a</mi><mi>n</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>t</mi><mi>a</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow></mrow></mfrac></mrow><mo>=</mo><mn>0.97</mn><mspace linebreak=”newline” /><mtext> between </mtext><mn>0</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow><mo>≤</mo><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>≤</mo><mn>360</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow></math>

$θ = 14.7 °, 74.7 °, 134.7 °, 194.7 °, 254.7 °, 314.7 °$
$θ = 29.7 °, 89.7 °, 149.7 °, 209.7 °, 269.7 °, 329.7 °$
$θ = 7.4 °, 37.4 °, 67.4 °, 97.4 °, 127.4 °, 157.4 °$
$θ = 29.4 °, 149.4 °, 269.4 °, 389.4 °, 509.4 °, 629.4 °$

<math xmlns=”http://www.w3.org/1998/Math/MathML”><mtext>Solve </mtext><mi>c</mi><mi>o</mi><mi>s</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>c</mi><mi>o</mi><mi>s</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>−</mo><mi>s</mi><mi>i</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>s</mi><mi>i</mi><mi>n</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>=</mo><mo>−</mo><mn>0.43</mn><mspace linebreak=”newline” /><mtext> between </mtext><mn>0</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow><mo>≤</mo><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>≤</mo><mn>360</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow></math>

$θ = 38.5 °, 81.5 °, 158.5 °, 201.5 °, 278.5 °, 321.5 °$
$θ = 53.5 °, 96.5 °, 173.5 °, 216.5 °, 293.5 °, 336.5 °$
$θ = 57.7 °, 122.3 °, 237.7 °, 302.3 °, 417.7 °, 482.3 °$
$θ = 23.5 °, 66.5 °, 143.5 °, 186.5 °, 263.5 °, 306.5 °$

<math xmlns=”http://www.w3.org/1998/Math/MathML”><mtext>Solve </mtext><mrow class=”MJX-TeXAtom-ORD”><mfrac><mrow class=”MJX-TeXAtom-ORD”><mi>t</mi><mi>a</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>+</mo><mi>t</mi><mi>a</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow></mrow><mrow class=”MJX-TeXAtom-ORD”><mn>1</mn><mo>+</mo><mi>t</mi><mi>a</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>t</mi><mi>a</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow></mrow></mfrac></mrow><mo>=</mo><mo>−</mo><mn>0.98</mn><mspace linebreak=”newline” /><mtext> between </mtext><mn>0</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow><mo>≤</mo><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>≤</mo><mn>360</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow></math>

$θ = 33.9 °, 78.9 °, 123.9 °, 168.9 °, 213.9 °, 258.9 °, 303.9 °$
$θ = 63.9 °, 108.9 °, 153.9 °, 198.9 °, 243.9 °, 288.9 °, 333.9 °$
$θ = 67.8 °, 157.8 °, 247.8 °, 337.8 °, 427.8 °, 517.8 °, 607.8 °$
$θ = 50.8 °, 118.3 °, 185.8 °, 253.3 °, 320.8 °, 388.3 °, 455.8 °$

<math xmlns=”http://www.w3.org/1998/Math/MathML”><mtext>Solve </mtext><mi>s</mi><mi>i</mi><mi>n</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>c</mi><mi>o</mi><mi>s</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>+</mo><mi>c</mi><mi>o</mi><mi>s</mi><mn>2</mn><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mi>s</mi><mi>i</mi><mi>n</mi><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>=</mo><mn>0.68</mn><mspace linebreak=”newline” /><mtext> between </mtext><mn>0</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow><mo>≤</mo><mrow class=”MJX-TeXAtom-ORD”><mo>θ</mo></mrow><mo>≤</mo><mn>360</mn><mrow class=”MJX-TeXAtom-ORD”><mo>°</mo></mrow></math>

$θ = 14.3 °, 45.7 °, 134.3 °, 165.7 °, 254.3 °, 285.7 °$
$θ = 7.1 °, 22.9 °, 67.1 °, 82.9 °, 127.1 °, 142.9 °$
$θ = 9.5 °, 30.5 °, 89.5 °, 110.5 °, 169.5 °, 190.5 °$
$θ = - 0.7 °, 30.7 °, 119.3 °, 150.7 °, 239.3 °, 270.7 °$

Trigonometric Equations (using identities) in given intervals – Further Maths

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