Posted by Joe on Saturday, July 18, 2009 at 11:10pm.
assuming that 2cos^2x means 2(cos(x))^2
substitute using
(cos(x))^2 = 1 - (sin(x))^2
2(1 - (sin(x))^2) + 3sin(x) = 3
2 - 2(sin(x))^2 + 3sin(x) = 3
for clarity, let u = sin(x)
2 - 2u^2 + 3u = 3
rearranging...
2u^2 - 3 u + 1 = 0
Solve this quadratic to find the values of sin x that are solutions. Finally, determine the angles in the range that have that value of sin(x).
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