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Grade 11 · Trigonometry
Trig Identities & Reduction Formulae: Full Guide
MEMORANDUM
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Class: 
Date: 
Mark
  / 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Simplify sinθ · tanθ · cosθ. (simplify)
    (2)
    sinθ·(sinθ/cosθ)·cosθ = sin2θ✓✓ (2)
  2. 2
    Simplify (1 − sin2θ). (identity)
    (2)
    cos2θ✓✓ (2)
  3. 3
    Simplify cos2θ ⁄ (1 − sin2θ). (identity)
    (2)
    cos2θ/cos2θ = 1✓✓ (2)
  4. 4
    Prove tanθ · cosθ = sinθ. (prove)
    (2)
    (sinθ/cosθ)·cosθ = sinθ ✓✓✓ (2)
  5. 5
    In which quadrant are only sine positive? (CAST)
    (2)
    2nd quadrant✓✓ (2)
  6. 6
    sinθ = 0,5, θ in Q2. Is cosθ + or −? (CAST)
    (2)
    Q2 → cosine negative✓✓ (2)
  7. 7
    Simplify cos(180° − θ). (reduction)
    (2)
    −cosθ✓✓ (2)
  8. 8
    Simplify sin(360° − θ). (reduction)
    (2)
    −sinθ✓✓ (2)
  9. 9
    Exact value of sin 150°. (exact)
    (2)
    150° = 180−30, Q2 sine + → sin30° = 12✓✓ (2)
  10. 10
    Exact value of cos 210°. (exact)
    (2)
    210° = 180+30, Q3 cosine − → −cos30° = −3⁄2✓✓ (2)
TOTAL: 20 marks
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