Find all values of x in the interval of [ 0 , 360 ) that satifsy each equation. Round approximatr answers to the nearest tenth of a degree.
1. sin x cos x + 2 cos x = 3 sin x + 6
2. 8 cos^4 x - 10 cos^2 x + 3 = 0
Thank you.
+128406 1. sin x cos x + 2 cos x = 3 sin x + 6
sinxcosx + 2cos x - 3sinx - 6 = 0
(cosx -3) (sin x + 2) = 0
No solutions cosx - 3 = 0 implies that cos x = 3 [impossible]
And sin x + 2 = 0 implies that sin x = - 2 [ also impossible ]
+128406 2. 8 cos^4 x - 10 cos^2 x + 3 = 0
(4cos^2x - 3) ( 2cos^2x - 1) = 0
4cos^2x - 3 = 0
4cos^2x = 3
cos^2x = 3/4
cosx = √3/2 and this happens at x = 30° and x = 330°
cos x = - √3/2 and this happens at x = 150° and x = 210°
2cos^2x - 1 = 0
2cos^2x = 1
cos^2 x = 1/2
cos x = 1/√2 and this happens at x = 45° and x = 315°
cos x = -1 /√2 and this happens at x =135° and x = 225°
