Moderate -0.3 This question requires recognizing the complementary angle identity (sin θ = cos(90° - θ)) and solving a linear equation in x, but the fractional coefficient and degree arithmetic make it slightly more involved than a basic trig equation. It's a standard FP1 general solution question with one moderately tricky step, placing it just below average difficulty.
4(a) | $\sin(70 - \frac{2}{3}x) = \cos 20 = \sin 70°$ | B1 | Watch out for the many correct different forms of the general solutions. OE $\cos20 = \sin70$; or $\cos20 = \sin110$ etc PI
4(a) | $\sin(70 - \frac{2}{3}x) = \sin 110°$ | B1 | OE; Use of a correct angle, in degrees, in other relevant quadrant PI
4(a) | $70 - \frac{2}{3}x = 360n° + "70°"$ | M1 | OE; Either one, showing a correct use of 360n in forming a general solution. Condone 2πn in place of 360n
4(a) | $70 - \frac{2}{3}x = 360n° + "110°"$ | |
4(a) | $x = -\frac{3}{2}(70° - 70° - 360n°)$ | m1 | OE to $x = -\frac{3}{2}(\pm 360n + \alpha - 70)$ OE, where α is from c's $\sin \alpha = \cos20$. Condone 2πn in place of 360n. OE eg 540n°, 540n°−60°. Condone 0 ≡ 540n for ± 540n. If not A2, award (i) A1 for either correct unsimplified full general solution or (ii) A1F for correct ft full general solution, ft c's wrong angle(s) after award of B0, may be left in unsimplified form(s) or (iii) A1 for 'correct' simplified full general solution but with radians present
4(a) | $x = \frac{3}{2}(70° - 110° - 360n°)$ | |
4(a) | $x = -540n°; \quad x = -540n° - 60$ | A2,1,0 |