TMUA Official 2016 Paper 2 · Question 17

Consider these simultaneous equations, where $c$ is a constant:

y=3\sin x+2

y=x+c

Which of the following statements is/are true?

1 For some value of $c$ : there is exactly one solution with $0\leq x\leq\pi$ and there is at least one solution with $-\pi<x<0$ .
2 For some value of $c$ : there is exactly one solution with $0\leq x\leq\pi$ and there are no solutions with $-\pi<x<0$ .
3 For some value of $c$ : there is exactly one solution with $0\leq x\leq\pi$ and there are no solutions with $x>\pi$ .

Anone

B1 only

C2 only

D3 only

E1 and 2 only

F1 and 3 only

G2 and 3 only

H1, 2 and 3

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