TMUA Practice · 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 $0 \leq x \leq π$ and there is at least one solution with $- π < x < 0$ .

2 For some value of $c$ : there is exactly one solution with $0 \leq x \leq π$ and there are no solutions with $- π < x < 0$ .

3 For some value of $c$ : there is exactly one solution with $0 \leq x \leq π$ and there are no solutions with $x > π$ .