What is the general solution for sin^2(x)-6sin(x)+3=0 ?

The general solution for sin^2(x)-6sin(x)+3=0 is x=0.58297…+2pin,x=pi-0.58297…+2pin

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sin^2(x)-6sin(x)+3=0

sin^{2} (x) - 6 sin (x) + 3 = 0

x = 0.58297 \dots + 2 πn, x = π - 0.58297 \dots + 2 πn

Solution steps

sin^{2} (x) - 6 sin (x) + 3 = 0

Solve by substitution

sin (x) = 3 + 6, sin (x) = 3 - 6

sin (x) = 3 + 6 :

No Solution

sin (x) = 3 - 6 : x = arcsin (3 - 6) + 2 πn, x = π - arcsin (3 - 6) + 2 πn

Combine all the solutions

x = arcsin (3 - 6) + 2 πn, x = π - arcsin (3 - 6) + 2 πn

Show solutions in decimal form

x = 0.58297 \dots + 2 πn, x = π - 0.58297 \dots + 2 πn

12 csc^{2} (θ) - csc (θ) - 1 = 0

2 cos (2 θ) - 4 cos (θ) + 2 = - 1

cos (a) = \frac{1}{sin ( a )}

sin (a) = cos (a)

tan (a) = 2.0503

What is the general solution for sin^2(x)-6sin(x)+3=0 ?
The general solution for sin^2(x)-6sin(x)+3=0 is x=0.58297…+2pin,x=pi-0.58297…+2pin