What is the general solution for 2+cos^2(x)=-5sin(x) ?

The general solution for 2+cos^2(x)=-5sin(x) is x=-0.57207…+2pin,x=pi+0.57207…+2pin

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2+cos^2(x)=-5sin(x)

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

x = - 0.57207 \dots + 2 πn, x = π + 0.57207 \dots + 2 πn

Solution steps

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

Subtract

- 5 sin (x)

from both sides

2 + cos^{2} (x) + 5 sin (x) = 0

Rewrite using trig identities

3 - sin^{2} (x) + 5 sin (x) = 0

Solve by substitution

sin (x) = - \frac{- 5 + 37}{2}, sin (x) = \frac{5 + 37}{2}

sin (x) = - \frac{- 5 + 37}{2} : x = arcsin (- \frac{- 5 + 37}{2}) + 2 πn, x = π + arcsin (\frac{- 5 + 37}{2}) + 2 πn

sin (x) = \frac{5 + 37}{2} :

No Solution

Combine all the solutions

x = arcsin (- \frac{- 5 + 37}{2}) + 2 πn, x = π + arcsin (\frac{- 5 + 37}{2}) + 2 πn

Show solutions in decimal form

x = - 0.57207 \dots + 2 πn, x = π + 0.57207 \dots + 2 πn

tan^{5} (x) tan^{2} (x) = 1

\frac{sin ^{2} ( a ) + 1}{( 1 + tan ^{2} ( a ) )} = 1

tan (a) = \frac{5}{9}, b = 6

sin^{3} (x) sin^{2} (x) sin (x) = 0

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

What is the general solution for 2+cos^2(x)=-5sin(x) ?
The general solution for 2+cos^2(x)=-5sin(x) is x=-0.57207…+2pin,x=pi+0.57207…+2pin