Answer:
x=30°, 150°, 210° & 330°
Step-by-step explanation:
4cos²x - 3 = 0
=> Add 3 to both sides, then
4cos²x = 3
=> Divide both sides by 4, then
cos²x = 3/4
=> Square root both sides, then
cos x = ± √(3/4)
cos x = ± √3/2
cos x = - √3/2 or √3/2
=> Starting cos x = - √3/2, we calculate thus:
x = cos^-1 (- √3/2)
x = - cos^-1 (√3/2)
=> In trigonometry, cos^-1 of √3/2 is 30° but the -ve arc - cos of a value denotes that the real value of x here can only be obtained from the 2nd & 3rd Quadrant of the unit circle, where the values of cos are -ve, then
2nd Quadrant: 180° - 30° = 150°...
3rd Quadrant: 180° + 30° = 210°...
=> Moving on to x = cos^-1 (√3/2), we calculate thus:
x = 30°
=> In the unit circle of the 4 Quadrants, the 4th Quadrant has the cos of all values to be +ve, then
4th Quadrant: 360° - 30° = 330°...
Hence the real values of x in degrees are 30°, 150°, 210° & 330°
