WAEC Further Mathematics 2022 Theory — Question 4

Model answer

Using cos2x=1−2sin²x: 3(1−2sin²x)−sinx=0 → 6sin²x+sinx−3=0. By the quadratic formula: sinx = [−1±√(1+72)]/12 = (−1±√73)/12, giving sinx=0.6287 or sinx=−0.7953. sinx=0.6287 → x=38.95° (1st quadrant) or x=180−38.95=141.05° (2nd quadrant). sinx=−0.7953 → x=180+52.68=232.68° (3rd quadrant) or x=360−52.68=307.32° (4th quadrant). Thus x = 38.95°, 141.05°, 232.68° or 307.32°.