Higher June 2017 Paper 6 Q15
15
(a) Sketch the graph of \(y = \sin x\) for \(0^\circ \leqslant x \leqslant 360^\circ\).
[2]
(b) Solve the equation \(5 \sin x = -3\).
Give all of the solutions in the range \(0^\circ \leqslant x \leqslant 360^\circ\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Correct sketch with max at (90, 1) and min at (270, -1) and crossing \(x\)-axis at 0, 180 and 360 | 2 | M1 for correct shape starting at (0, 0) but inaccurate at roots and max/min. Needs at least one cycle, but may have more than one. | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 217° and 323° | 4 | B3 for one correct even if from trials OR M2 for [\(x =\)] −37 to −36.86 OR M1 for \(\sin x = -0.6\) oe If 0 scored SC1 answers summing to 540 to 3sf | Accept answers to greater accuracy 216.8[6…] and 323.1[3…] B3 for grads: [\(x =\)] (−41), 221, 319 OR B2 for grads: [\(x =\)] one of 221, 319 OR M1 implied for grads [\(x =\)] −41 or rads: [\(x =\)] −0.64[…] |