Nusret Balcı TMUA Paper 1 · Question 6

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Nusret Balcı TMUA Paper 1 · Q6

Paper 1TrigonometryAlgebra

Let $k\in\mathbb R$ . Consider the equation

(1+3\cos\theta)^2=k\cos2\theta,\qquad0^\circ\le\theta\le360^\circ.

For which values of $k$ does the equation have exactly four distinct solutions in the given interval?

k<-9

-9<k<-1

-1<k<0

0<k<1

1<k<9

k<0\text{ or }k>\frac72

k<0\text{ or }k>4

k<0\text{ or }k\ge16

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