TMUA 2016 Paper 2 Q17 — Worked Solution

P2·Trigonometry, Logic & Quantifiers·7.0Official · 2016 · Q17

sine-and-linegraphical-intersectionmulti-statement

Consider these simultaneous equations, where

c

is a constant:

y = 3 sin x + 2

and

y = x + c

. Consider the three statements:

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

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

III

For some value of

c

: there is exactly one solution with

0 \leq x \leq π

and there are no solutions with

x > π

Which of the above statements is/are true?

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