What is the general solution for 4sin^2(x)-7sin(x)+3=0 ?

The general solution for 4sin^2(x)-7sin(x)+3=0 is x= pi/2+2pin,x=0.84806…+2pin,x=pi-0.84806…+2pin

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4sin^2(x)-7sin(x)+3=0

4 sin^{2} (x) - 7 sin (x) + 3 = 0

x = \frac{π}{2} + 2 πn, x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

Solution steps

4 sin^{2} (x) - 7 sin (x) + 3 = 0

Solve by substitution

sin (x) = 1, sin (x) = \frac{3}{4}

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = \frac{3}{4} : x = arcsin (\frac{3}{4}) + 2 πn, x = π - arcsin (\frac{3}{4}) + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = arcsin (\frac{3}{4}) + 2 πn, x = π - arcsin (\frac{3}{4}) + 2 πn

Show solutions in decimal form

x = \frac{π}{2} + 2 πn, x = 0.84806 \dots + 2 πn, x = π - 0.84806 \dots + 2 πn

2 sin (x - 1 0^{\circ}) = - 0.4

cot^{2} (2 x - \frac{π}{3}) = \frac{1}{3}

sin (2 x) = 0.8, - 18 0^{\circ} \leq x \leq 18 0^{\circ}

\frac{tan ( x )}{1 + tan ( x )} = 0

1 - cos (x) + sin (x) = 0

What is the general solution for 4sin^2(x)-7sin(x)+3=0 ?
The general solution for 4sin^2(x)-7sin(x)+3=0 is x= pi/2+2pin,x=0.84806…+2pin,x=pi-0.84806…+2pin