trig
posted by Anonymous on .
Find all the solutions of 2 sinx=1cosx in the interval from 0° ≤x<360°

square both sides ...
4 sin^2 x = 1  2 cosx + cos^2 x
4(1  cos^2 x) = 1  2cosx + cos^2 x
4  4cos^2 x = 1  2cosx + cos^2 x
5 cos^2 x  2cosx  3= 0
(cosx  1)(5cosx + 3) = 0
cosx = 1 or cosx = 3/5
x = 0 or 360, or x = 126.9° or 233.1°
since I squared, all answers must be checked:
if x=0, LS = 2sin0 = 0
RS = 1  cos0 = 0, good
if x= 360
LS = 2sin360 = 0
RS = 1  cos360 = 0, good
if x = 126.9
LS = 2sin126.9 = 1.6
RS = 1  cos126.9 = 1(3/5) = 1.6 , good
if x = 233.1°
LS = 2sin233.1 = 1.6
RS = 1  cos233.1 = 1.6 , no good
x = 0, 126.9, and 360 
except 0°≤x<360°