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Grade 11 · Trigonometry
Trig Identities & Reduction Formulae: Full Guide
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  / 23

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

  1. 1
    Simplify sinθ · tanθ · cosθ, and state the restriction on θ. (simplify)
    (3)
  2. 2
    Simplify (1 − sin2θ). (identity)
    (1)
  3. 3
    Simplify cos2θ/(1 − sin2θ). (identity)
    (2)
  4. 4
    Prove tanθ · cosθ = sinθ, and say where the identity does not hold. (prove)
    (3)
  5. 5
    In which quadrant are only sine positive? (CAST)
    (1)
  6. 6
    sinθ = 0,5, θ in Q2. Is cosθ + or −? (CAST)
    (1)
  7. 7
    Simplify cos(180° − θ). (reduction)
    (1)
  8. 8
    Simplify sin(360° − θ). (reduction)
    (1)
  9. 9
    Exact value of sin 150°. (exact)
    (2)
  10. 10
    Exact value of cos 210°. (exact)
    (2)
  11. 11
    For which values of θ is tanθ undefined? Give the general answer.
    (2)
  12. 12
    For θ ∈ [0° ; 360°], state the values for which (sinθ × tanθ)/cosθ is undefined.
    (2)
  13. 13
    Explain why the restriction must be read off the ORIGINAL expression and not the simplified one.
    (2)
TOTAL: 23 marks
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