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tmua.me Medium Set F Paper 2 · Q16

Paper 2TrigonometryAlgebra

For which real values of kk does the equation

sin⁡2θ−(k+1)sin⁡θ+k24=0\sin^2\theta-(k+1)\sin\theta+\frac{k^2}{4}=0

have exactly four distinct solutions satisfying 0≤θ≤2π0\leq\theta\leq2\pi?

A−12<k<0-\dfrac12<k<0
B−12<k≤0-\dfrac12<k\leq0
C−12≤k≤0-\dfrac12\leq k\leq0
D−12<k<1-\dfrac12<k<1
Ek<0k<0
F0≤k<40\leq k<4

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