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Which of the following is IMPOSSIBLE for a real angle θ?

Competition practiceTrigonometry
  • Asinθ = 0.9
  • Bcosθ = −0.9
  • Ctanθ = 100
  • Dsecθ = 0.9

Step-by-Step Solution

secθ = 1/cosθ and |cosθ| ≤ 1, so |secθ| is always at least 1 — the value 0.9 can never occur. Sine and cosine may be any number in [−1, 1] (so 0.9 and −0.9 are fine), and tanθ is unbounded, so 100 is attainable.
Answer: D) secθ = 0.9

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