How to solve \(\displaystyle{3}{{\sin}^{{2}}{x}}-{5}{\sin{{x}}}{\cos{{x}}}+{2}{{\cos}^{{2}}{x}}={0}\)

atenienseec1p

atenienseec1p

Answered question

2022-04-01

How to solve
3sin2x5sinxcosx+2cos2x=0

Answer & Explanation

disolutoxz61

disolutoxz61

Beginner2022-04-02Added 12 answers

here is way to solve the equation
3sin3t5sintcost+2cos2t=0 (1)
we will introduce
x=cost, y=sint, x2+y2=1
now we have
0=3y35xy+2x2=3y(1x2)5xy+2x2=y(3x2+5x3)+2x2
solving for y gives
y=2x23x2+5x3 (2)
the graphs of (1) and (2) intersect at four points in the first, third and fourth quadrants. the coordinates
x=0.912, 0.563, 0.937, 0.418
the corresponding angles in radians are
0.422, 0.9727, 3.498, 5.144
Regan Gallegos

Regan Gallegos

Beginner2022-04-03Added 9 answers

convert this equation in tan(x2) and set t=tan(x2)
24(tan(x2))3(1+(tan(x2))2)310tan(x2)(1(tan(x2))2)(1+(tan(x2))2)2+2(1(tan(x2))2)2(1+(tan(x2))2)2=0

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