What is the general solution for 6sin^2(x)-5sin(x)=0 ?

The general solution for 6sin^2(x)-5sin(x)=0 is x=0.98511…+2pin,x=pi-0.98511…+2pin,x=2pin,x=pi+2pin

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6sin^2(x)-5sin(x)=0

6 sin^{2} (x) - 5 sin (x) = 0

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

6 sin^{2} (x) - 5 sin (x) = 0

Solve by substitution

sin (x) = \frac{5}{6}, sin (x) = 0

sin (x) = \frac{5}{6} : x = arcsin (\frac{5}{6}) + 2 πn, x = π - arcsin (\frac{5}{6}) + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = arcsin (\frac{5}{6}) + 2 πn, x = π - arcsin (\frac{5}{6}) + 2 πn, x = 2 πn, x = π + 2 πn

Show solutions in decimal form

x = 0.98511 \dots + 2 πn, x = π - 0.98511 \dots + 2 πn, x = 2 πn, x = π + 2 πn

sinh (4 x) = \frac{3}{4}

tan (x) + sec (x) = 3

cos^{2} (3 x + \frac{π}{4}) = \frac{3}{4}

2 sin (\frac{π}{3} - x) - 1 = 0

- 2 sin (x) - 1 = 0

What is the general solution for 6sin^2(x)-5sin(x)=0 ?
The general solution for 6sin^2(x)-5sin(x)=0 is x=0.98511…+2pin,x=pi-0.98511…+2pin,x=2pin,x=pi+2pin