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

The general solution for sin^2(x)-sin(x)=1 is x=-0.66623…+2pin,x=pi+0.66623…+2pin

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sin^2(x)-sin(x)=1

sin^{2} (x) - sin (x) = 1

x = - 0.66623 \dots + 2 πn, x = π + 0.66623 \dots + 2 πn

Solution steps

sin^{2} (x) - sin (x) = 1

Solve by substitution

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

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

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

x = - 0.66623 \dots + 2 πn, x = π + 0.66623 \dots + 2 πn

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

cos (y) = \frac{1}{2}

tan (x) = \frac{cos ( x )}{sin ( x )}

4 tan (x) - 3 = 7 tan (x)

sin (x) = π

What is the general solution for sin^2(x)-sin(x)=1 ?
The general solution for sin^2(x)-sin(x)=1 is x=-0.66623…+2pin,x=pi+0.66623…+2pin