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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

tan (x) = \frac{- 3}{3}

tan (\frac{x}{3}) = \frac{3}{3}

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

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

- 5 (sec (x) - 2) (2 sin (x) + 3) = 0

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