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

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

No Solution

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

x, c sin (m x) m = \frac{nπ}{a}

x, - 0.3 \cdot cos (x) + sin (x) = 0.10618

6 tan (x) = 4

3 tan (x) + cot (x) - 5 csc (x) = 0

3 cos^{2} (x) = 1 - 5 sin (x)

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