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JAMB 2003 · UME · Q26

Which of the following is the graph of sin⁡θ\sin\theta for −π2≤θ≤3π2-\frac{\pi}{2} \le \theta \le \frac{3\pi}{2}?

−π/2π/2π3π/21−1A.−π/2π/2π3π/21−1B.−π/2π/2π3π/21−1C.−π/2π/2π3π/21−1D.
Worked solution (try it first)
  1. Work out the key values: sin⁡(−π2)=−1\sin(-\frac{\pi}{2}) = -1, sin⁡0=0\sin 0 = 0, sin⁡π2=1\sin\frac{\pi}{2} = 1, sin⁡π=0\sin\pi = 0 and sin⁡3π2=−1\sin\frac{3\pi}{2} = -1.
  2. So the graph starts at −1-1, passes through the origin, peaks at 1 when θ=π2\theta = \frac{\pi}{2} and falls back to −1-1 at 3π2\frac{3\pi}{2}.
  3. Only graph C does this, so the answer is option C.

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