What is the general solution for 9sin^2(x)-6sin(x)+1=0 ?

The general solution for 9sin^2(x)-6sin(x)+1=0 is x=0.33983…+2pin,x=pi-0.33983…+2pin

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9sin^2(x)-6sin(x)+1=0

9 sin^{2} (x) - 6 sin (x) + 1 = 0

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

Solution steps

9 sin^{2} (x) - 6 sin (x) + 1 = 0

Solve by substitution

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

sin (x) = \frac{1}{3} : x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

y, ln (x) = arctan (\frac{y}{x})

cos (a) + 1 = 4 cos (a) + 1

6 cos (x) + 3 sin (x) = 5

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

sin (2 x) + cos (x) = 0, x \leq 2 π, 0

What is the general solution for 9sin^2(x)-6sin(x)+1=0 ?
The general solution for 9sin^2(x)-6sin(x)+1=0 is x=0.33983…+2pin,x=pi-0.33983…+2pin