What is the general solution for 1-sin^2(x)+sin(x)=0 ?

The general solution for 1-sin^2(x)+sin(x)=0 is x=-0.66623…+2pin,x=pi+0.66623…+2pin

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1-sin^2(x)+sin(x)=0

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

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

Solution steps

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

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

sin (4 x) = \frac{3}{4}

23 sec (x) + 4 = 0

\frac{sin ( θ )}{60} = \frac{sin ( 4 5 ^{\circ} )}{246.26}

6 cos (θ) = 32

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

What is the general solution for 1-sin^2(x)+sin(x)=0 ?
The general solution for 1-sin^2(x)+sin(x)=0 is x=-0.66623…+2pin,x=pi+0.66623…+2pin