Circular (trigonometric) functions — A/L Combined Mathematics

How do I practise Circular (trigonometric) functions?

1 question with a worked solution

1. Which of the following trigonometric identities expresses sin(2θ) in terms of tan(θ)?
   1. A) (2 tan θ) / (1 - tan² θ)
   2. B) (2 tan θ) / (1 + tan² θ)
   3. C) (1 - tan² θ) / (1 + tan² θ)
   4. D) (tan θ) / (1 + tan² θ)
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   Correct answer: B) (2 tan θ) / (1 + tan² θ)

   Starting from the double angle identity sin(2θ) = 2 sin θ cos θ = 2 (sin θ / cos θ) cos² θ = 2 tan θ / sec² θ. Since sec² θ = 1 + tan² θ, we obtain sin(2θ) = (2 tan θ) / (1 + tan² θ).

   Show worked solution

   Step 1: sin(2θ) = 2 sin θ cos θ. Step 2: Divide by cos² θ and multiply by cos² θ: 2 tan θ cos² θ = (2 tan θ) / sec² θ. Step 3: Since sec² θ = 1 + tan² θ: sin(2θ) = (2 tan θ) / (1 + tan² θ). Answer: (2 tan θ) / (1 + tan² θ).
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Circular (trigonometric) functions fit in the syllabus?

Year 1 · Term 2