What is the general solution for 49.55*sqrt(1-sin^2(θ))-30sin(θ)=1.225 ?

The general solution for 49.55*sqrt(1-sin^2(θ))-30sin(θ)=1.225 is θ=1.00522…+2pin,θ=pi-1.00522…+2pin

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49.55*sqrt(1-sin^2(θ))-30sin(θ)=1.225

49.55 \cdot 1 - sin^{2} (θ) - 30 sin (θ) = 1.225

θ = 1.00522 \dots + 2 πn, θ = π - 1.00522 \dots + 2 πn

Solution steps

49.55 1 - sin^{2} (θ) - 30 sin (θ) = 1.225

Solve by substitution

sin (θ) = \frac{- 0.02190 \dots + 2.92573 \dots}{2}

sin (θ) = \frac{- 0.02190 \dots + 2.92573 \dots}{2} : θ = arcsin (\frac{- 0.02190 \dots + 2.92573 \dots}{2}) + 2 πn, θ = π - arcsin (\frac{- 0.02190 \dots + 2.92573 \dots}{2}) + 2 πn

Combine all the solutions

θ = arcsin (\frac{- 0.02190 \dots + 2.92573 \dots}{2}) + 2 πn, θ = π - arcsin (\frac{- 0.02190 \dots + 2.92573 \dots}{2}) + 2 πn

Show solutions in decimal form

θ = 1.00522 \dots + 2 πn, θ = π - 1.00522 \dots + 2 πn

cos (2 x) + sin (x) - 1 = 0

x, e^{c o s (y)} - e^{s i n (x)} = sin (y)

5 + tan (θ) = 4

arctan (e^{x}) = 0

cos (x) = 3 - cos (x)

What is the general solution for 49.55*sqrt(1-sin^2(θ))-30sin(θ)=1.225 ?
The general solution for 49.55*sqrt(1-sin^2(θ))-30sin(θ)=1.225 is θ=1.00522…+2pin,θ=pi-1.00522…+2pin