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

The general solution for sin^2(x)=-cos(x) is x=2.23703…+2pin,x=-2.23703…+2pin

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

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

x = 2.23703 \dots + 2 πn, x = - 2.23703 \dots + 2 πn

Solution steps

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

Subtract

- cos (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

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

No Solution

Combine all the solutions

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

Show solutions in decimal form

x = 2.23703 \dots + 2 πn, x = - 2.23703 \dots + 2 πn

arctan (x) = \frac{π}{12}

8 sin^{2} (w) + 10 sin (w) + 3 = 0

2 - 2 cos^{2} (x) = 2 sin^{2} (\frac{x}{2})

(\frac{2}{2}) (cos (θ) + sin (θ)) = 0

12 sin (x) - 2 = 2 + 8 sin (x)

What is the general solution for sin^2(x)=-cos(x) ?
The general solution for sin^2(x)=-cos(x) is x=2.23703…+2pin,x=-2.23703…+2pin