What is the general solution for 5sin^2(x)-11sin(x)+2=0 ?

The general solution for 5sin^2(x)-11sin(x)+2=0 is x=0.20135…+2pin,x=pi-0.20135…+2pin

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5sin^2(x)-11sin(x)+2=0

5 sin^{2} (x) - 11 sin (x) + 2 = 0

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

Solution steps

5 sin^{2} (x) - 11 sin (x) + 2 = 0

Solve by substitution

sin (x) = 2, sin (x) = \frac{1}{5}

sin (x) = 2 :

No Solution

sin (x) = \frac{1}{5} : x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn

Combine all the solutions

x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn

Show solutions in decimal form

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

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

3 sin (a) + cos (a) = 1

4 cos^{2} (x) + 3 = 2 (3 + 1)

2 tan^{2} (x) + cot^{2} (x) - 3 = 0

\frac{( 2 sin ( x ) - 1 )}{( sin ( x ) + 5 )} = 0

What is the general solution for 5sin^2(x)-11sin(x)+2=0 ?
The general solution for 5sin^2(x)-11sin(x)+2=0 is x=0.20135…+2pin,x=pi-0.20135…+2pin