Solve the equations below to the nearest degree.

Question

 

1. Solve the following equations, to the nearest degree if needed, for 0° ≤ x ≤ 360°. (14 marks)
   1. sin²x = ½
   2. cos²x = - cosx
   3. 6sin²x - 11sinx + 4 = 0
   4. 3cos²x - 2cosx - 1 = 0

Answer 1

a) sin²(x)=½, sin(x)=±1/√2, x=π/4, 3π/4, 5π/4, 7π/4 (45°, 135°, 225°, 315°)

b) cos²(x)=-cos(x), cos(x)(cos(x)+1)=0, cos(x)=0, x=π/2, 3π/2 (90°, 270°); cos(x)=-1, x=π (180°).

c) 6sin²(x)-11sin(x)+4=0=(2sin(x)-1)(3sin(x)-4), sin(x)=½, x=π/6, 5π/6 (30°, 150°).

d) 3cos²(x)-2cos(x)-1=0=(cos(x)-1)(3cos(x)+1), cos(x)=1, x=0, 2π (0°, 360°); cos(x)=-⅓, x=1.91 (109°), 4.37 (251°).