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

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

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

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

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

Solution steps

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

Subtract

- cos^{2} (x)

from both sides

sin (x) + cos^{2} (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

sin (x) + \frac{2}{2} = 0

2 csc (θ) = 4 cos (θ)

\frac{6}{5} arccos (\frac{y}{6}) = π

cos (x) = \frac{154}{212.85}

4 sin^{2} (x) - 2 = 0, 0 \leq x \leq 2 π

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