tmua 2016 Q17

tmua · Uk · paper2 1 marks Curve Sketching Number of Solutions / Roots via Curve Analysis
Consider these simultaneous equations, where $c$ is a constant:
$$\begin{aligned} & y = 3 \sin x + 2 \\ & y = x + c \end{aligned}$$
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 $x > \pi$.
& D & 17 & H
Consider these simultaneous equations, where $c$ is a constant:

$$\begin{aligned}
& y = 3 \sin x + 2 \\
& y = x + c
\end{aligned}$$

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 $x > \pi$.