What is the general solution for 5sin^2(x)=3sin(x)+2 ?

The general solution for 5sin^2(x)=3sin(x)+2 is x= pi/2+2pin,x=-0.41151…+2pin,x=pi+0.41151…+2pin

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5sin^2(x)=3sin(x)+2

5 sin^{2} (x) = 3 sin (x) + 2

x = \frac{π}{2} + 2 πn, x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn

Solution steps

5 sin^{2} (x) = 3 sin (x) + 2

Solve by substitution

sin (x) = 1, sin (x) = - \frac{2}{5}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = - \frac{2}{5} : x = arcsin (- \frac{2}{5}) + 2 πn, x = π + arcsin (\frac{2}{5}) + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = arcsin (- \frac{2}{5}) + 2 πn, x = π + arcsin (\frac{2}{5}) + 2 πn

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn

sin^{2} (x) = - (\frac{1}{2})

α, sin^{2} (3 α) = 0.56

(sin (x) - cos (x))^{2} = 1^{2}

tan (\frac{π}{2} - x) + 2 tan (\frac{π}{2} + x) = 1

\frac{11.0994}{cos ( x )} = \frac{3.5355}{sin ( x )}

What is the general solution for 5sin^2(x)=3sin(x)+2 ?
The general solution for 5sin^2(x)=3sin(x)+2 is x= pi/2+2pin,x=-0.41151…+2pin,x=pi+0.41151…+2pin