6.9 Know and use tan θ = sin θ / cos θ and sin2θ + cos2θ = 1 Quiz: AQA Further Maths, Unit 6

The 20 questions

1. Which identity links tan θ with sin θ and cos θ?

   • tan θ = sin θ × cos θ
   • tan θ = sin θ + cos θ
   • tan θ = cos θ ÷ sin θ
   • tan θ = sin θ ÷ cos θ

2. Which is the Pythagorean identity for sin θ and cos θ?

   • sin²θ + cos²θ = 1
   • tan²θ + 1 = sin²θ
   • sin θ + cos θ = 1
   • sin²θ − cos²θ = 1

3. If sin θ = 0.6, what is the value of cos²θ?

   • 0.16
   • 0.64
   • 0.36
   • 0.4

4. Simplify sin θ ÷ cos θ.

   • tan θ
   • cot θ
   • sin θ cos θ
   • 1

5. Which expression is equal to 1 − cos²θ?

   • tan²θ
   • sin θ cos θ
   • cos²θ − 1
   • sin²θ

6. Which expression is equal to cos θ ÷ sin θ?

   • tan θ
   • sin θ ÷ cos θ
   • 1 ÷ tan θ
   • 1 ÷ sin θ

7. Which expression equals tan θ × cos θ?

   • tan θ ÷ cos θ
   • cos θ
   • sin θ
   • 1

8. Which expression is equal to 1 + tan²θ?

   • 1 ÷ cos²θ
   • 1 ÷ sin²θ
   • cos²θ
   • sin²θ

9. Simplify (1 − cos²θ) ÷ sin θ, assuming sin θ ≠ 0.

   • sin²θ
   • sin θ
   • cos θ
   • 1

10. If sin θ = 0.8 and θ is acute, what is tan θ exactly?

    • 4/3
    • 0.64
    • 3/4
    • 0.8

11. Simplify (sin θ + cos θ)² − 2 sin θ cos θ.

    • sin²θ − cos²θ
    • 1
    • 2
    • sin θ cos θ

12. Simplify tan θ × cos θ ÷ sin θ, assuming the expression is defined.

    • 1
    • tan θ
    • cos θ
    • sin θ

13. Given tan θ = 2 and cos θ = 1/√5 with cos θ positive, find sin θ.

    • 2/√5
    • −2/√5
    • 1/√5
    • √5/2

14. Simplify (1 − sin θ)(1 + sin θ).

    • cos²θ
    • sin²θ
    • 1 − 2 sin θ
    • 1 + sin²θ

15. Simplify 1 ÷ (1 + tan²θ), assuming cos θ ≠ 0.

    • cos²θ
    • sin²θ
    • 1
    • tan²θ

16. Given sin θ = 5/13, find cos²θ.

    • 25/169
    • 119/169
    • 144/169
    • 12/13

17. Simplify tan θ + 1 ÷ tan θ, assuming the expression is defined.

    • sin θ cos θ
    • 1 ÷ (sin θ + cos θ)
    • 1 ÷ (sin θ cos θ)
    • sin θ ÷ cos θ

18. Simplify sin⁴θ − cos⁴θ.

    • sin²θ − cos²θ
    • cos²θ − sin²θ
    • 1
    • sin²θ + cos²θ

19. Given tan θ = 2 and sin θ negative, with 0° ≤ θ < 360°, what is cos θ?

    • 1/√5 (about 0.447)
    • √5/2
    • −1/√5 (about −0.447)
    • −2/√5 (about −0.894)

20. For cos θ ≠ 0, what does cos θ × (1 + tan²θ) simplify to?

    • 1 ÷ cos θ
    • 1 ÷ cos²θ
    • sin θ ÷ cos θ
    • cos θ

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