What is the general solution for cos^2(θ)+2sin(θ)+1=0 ?

The general solution for cos^2(θ)+2sin(θ)+1=0 is θ=-0.82132…+2pin,θ=pi+0.82132…+2pin

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cos^2(θ)+2sin(θ)+1=0

cos^{2} (θ) + 2 sin (θ) + 1 = 0

θ = - 0.82132 \dots + 2 πn, θ = π + 0.82132 \dots + 2 πn

Solution steps

cos^{2} (θ) + 2 sin (θ) + 1 = 0

Rewrite using trig identities

2 - sin^{2} (θ) + 2 sin (θ) = 0

Solve by substitution

sin (θ) = 1 - 3, sin (θ) = 1 + 3

sin (θ) = 1 - 3 : θ = arcsin (1 - 3) + 2 πn, θ = π + arcsin (- 1 + 3) + 2 πn

sin (θ) = 1 + 3 :

No Solution

Combine all the solutions

θ = arcsin (1 - 3) + 2 πn, θ = π + arcsin (- 1 + 3) + 2 πn

Show solutions in decimal form

θ = - 0.82132 \dots + 2 πn, θ = π + 0.82132 \dots + 2 πn

arcsec (x) = arcsec (2)

tan^{2} (x) + (3 - 1) tan (x) - 3 = 0

sin (θ) = \frac{2}{7}

2 sec (x) - 5 = 0

tan (a) + cot (a) = sec (a) cos (a)

What is the general solution for cos^2(θ)+2sin(θ)+1=0 ?
The general solution for cos^2(θ)+2sin(θ)+1=0 is θ=-0.82132…+2pin,θ=pi+0.82132…+2pin