What is the general solution for 8sin^2(u)+6sin(u)-9=0 ?

The general solution for 8sin^2(u)+6sin(u)-9=0 is u=0.84806…+2pin,u=pi-0.84806…+2pin

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8sin^2(u)+6sin(u)-9=0

8 sin^{2} (u) + 6 sin (u) - 9 = 0

u = 0.84806 \dots + 2 πn, u = π - 0.84806 \dots + 2 πn

Solution steps

8 sin^{2} (u) + 6 sin (u) - 9 = 0

Solve by substitution

sin (u) = \frac{3}{4}, sin (u) = - \frac{3}{2}

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

sin (u) = - \frac{3}{2} :

No Solution

Combine all the solutions

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

Show solutions in decimal form

u = 0.84806 \dots + 2 πn, u = π - 0.84806 \dots + 2 πn

sin (x) = 2 tan (x)

cos (θ) = \frac{1}{5}

sin (\frac{x}{2}) - cos (x) = 0

3 sin (x) = 3 - 3 cos (x)

0 = 1 - 2 cos (x)

What is the general solution for 8sin^2(u)+6sin(u)-9=0 ?
The general solution for 8sin^2(u)+6sin(u)-9=0 is u=0.84806…+2pin,u=pi-0.84806…+2pin