What is the general solution for 2+2sin(θ)=-4sin(θ) ?

The general solution for 2+2sin(θ)=-4sin(θ) is θ=-0.33983…+2pin,θ=pi+0.33983…+2pin

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2+2sin(θ)=-4sin(θ)

2 + 2 sin (θ) = - 4 sin (θ)

θ = - 0.33983 \dots + 2 πn, θ = π + 0.33983 \dots + 2 πn

Solution steps

2 + 2 sin (θ) = - 4 sin (θ)

Solve by substitution

sin (θ) = - \frac{1}{3}

sin (θ) = - \frac{1}{3} : θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

Combine all the solutions

θ = arcsin (- \frac{1}{3}) + 2 πn, θ = π + arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

θ = - 0.33983 \dots + 2 πn, θ = π + 0.33983 \dots + 2 πn

cos (θ) = \frac{( 5 )}{( 13 )}

2 sin (θ) + 3 = - csc (θ)

2 sin (\frac{2 x}{3}) - 2 = 0

tan (θ) = - \frac{1}{4}

\frac{1}{cos ( x ) + 1} + \frac{1}{cos ( x ) - 1} = 2 csc (x) cot (x)

What is the general solution for 2+2sin(θ)=-4sin(θ) ?
The general solution for 2+2sin(θ)=-4sin(θ) is θ=-0.33983…+2pin,θ=pi+0.33983…+2pin