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

The general solution for sin^2(x)-3sin(x)-2=0 is x=-0.59626…+2pin,x=pi+0.59626…+2pin

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

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

x = - 0.59626 \dots + 2 πn, x = π + 0.59626 \dots + 2 πn

Solution steps

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

Solve by substitution

sin (x) = \frac{3 + 17}{2}, sin (x) = \frac{3 - 17}{2}

sin (x) = \frac{3 + 17}{2} :

No Solution

sin (x) = \frac{3 - 17}{2} : x = arcsin (\frac{3 - 17}{2}) + 2 πn, x = π + arcsin (- \frac{3 - 17}{2}) + 2 πn

Combine all the solutions

x = arcsin (\frac{3 - 17}{2}) + 2 πn, x = π + arcsin (- \frac{3 - 17}{2}) + 2 πn

Show solutions in decimal form

x = - 0.59626 \dots + 2 πn, x = π + 0.59626 \dots + 2 πn

- 11 tan (x) + 1 = - 2 (4 + tan (x))

16 = - 10 cos (\frac{2 π}{150} t) + 10

2 cos (x) - 3 = 0, 0 \leq x \leq 2 π

sec^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

3 cos (\frac{x}{2}) + 3 = cos (\frac{x}{2})

What is the general solution for sin^2(x)-3sin(x)-2=0 ?
The general solution for sin^2(x)-3sin(x)-2=0 is x=-0.59626…+2pin,x=pi+0.59626…+2pin