What is the general solution for 7sin^2(θ)-16sin(θ)+9=0 ?

The general solution for 7sin^2(θ)-16sin(θ)+9=0 is θ= pi/2+2pin

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7sin^2(θ)-16sin(θ)+9=0

7 sin^{2} (θ) - 16 sin (θ) + 9 = 0

θ = \frac{π}{2} + 2 πn

Solution steps

7 sin^{2} (θ) - 16 sin (θ) + 9 = 0

Solve by substitution

sin (θ) = \frac{9}{7}, sin (θ) = 1

sin (θ) = \frac{9}{7} :

No Solution

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn

cos^{2} (x) - cos (x) - 6 = 0

8 cos (x) tan (x) = 3 tan (x)

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

0 = 1 - cos (2 x)

sec^{2} (x) + 2 = 3 sec (x)

What is the general solution for 7sin^2(θ)-16sin(θ)+9=0 ?
The general solution for 7sin^2(θ)-16sin(θ)+9=0 is θ= pi/2+2pin