What is the general solution for 3sin^2(x)-5sin(x)-2=0 ?

The general solution for 3sin^2(x)-5sin(x)-2=0 is x=-0.33983…+2pin,x=pi+0.33983…+2pin

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3sin^2(x)-5sin(x)-2=0

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

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

Solution steps

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

Solve by substitution

sin (x) = 2, sin (x) = - \frac{1}{3}

sin (x) = 2 :

No Solution

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

csc (x) = - \frac{2}{3}

sin (x^{2}) = \frac{1}{2}

0 = 4 - sec^{2} (x)

8 sin (x) = 0

sin (x) = \frac{1}{5} 5, cos (x) - tan (x)

What is the general solution for 3sin^2(x)-5sin(x)-2=0 ?
The general solution for 3sin^2(x)-5sin(x)-2=0 is x=-0.33983…+2pin,x=pi+0.33983…+2pin