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

The general solution for cos^2(x)+2sin(x)=0 is x=-0.42707…+2pin,x=pi+0.42707…+2pin

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

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

x = - 0.42707 \dots + 2 πn, x = π + 0.42707 \dots + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 1 - 2, sin (x) = 1 + 2

sin (x) = 1 - 2 : x = arcsin (1 - 2) + 2 πn, x = π + arcsin (- 1 + 2) + 2 πn

sin (x) = 1 + 2 :

No Solution

Combine all the solutions

x = arcsin (1 - 2) + 2 πn, x = π + arcsin (- 1 + 2) + 2 πn

Show solutions in decimal form

x = - 0.42707 \dots + 2 πn, x = π + 0.42707 \dots + 2 πn

cos (3 θ) = \frac{1}{2}

sin (3 x + 5) = cos (4 x + 1)

6 sin^{2} (θ) - 3 = 0

4 cos (x) - 4 sin (x) = 26

sin (x) = \frac{8}{9}

What is the general solution for cos^2(x)+2sin(x)=0 ?
The general solution for cos^2(x)+2sin(x)=0 is x=-0.42707…+2pin,x=pi+0.42707…+2pin