What is the general solution for 1.58*sin(34)=1(sin(θ)) ?

The general solution for 1.58*sin(34)=1(sin(θ)) is θ=1.08333…+360n,θ=180-1.08333…+360n

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1.58*sin(34)=1(sin(θ))

1.58 \cdot sin (3 4^{\circ}) = 1 (sin (θ))

θ = 1.08333 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 1.08333 \dots + 36 0^{\circ} n

Radians

θ = 1.08333 \dots + 2 πn, θ = π - 1.08333 \dots + 2 πn

Solution steps

1.58 sin (3 4^{\circ}) = 1 \cdot (sin (θ))

Switch sides

1 \cdot sin (θ) = 1.58 sin (3 4^{\circ})

Multiply:

1 \cdot sin (θ) = sin (θ)

sin (θ) = 1.58 sin (3 4^{\circ})

Apply trig inverse properties

sin (θ) = 1.58 sin (3 4^{\circ})

General solutions for

sin (θ) = 1.58 sin (3 4^{\circ})

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

θ = arcsin (1.58 sin (3 4^{\circ})) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (1.58 sin (3 4^{\circ})) + 36 0^{\circ} n

θ = arcsin (1.58 sin (3 4^{\circ})) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (1.58 sin (3 4^{\circ})) + 36 0^{\circ} n

Show solutions in decimal form

θ = 1.08333 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 1.08333 \dots + 36 0^{\circ} n

What is the general solution for 1.58*sin(34)=1(sin(θ)) ?
The general solution for 1.58*sin(34)=1(sin(θ)) is θ=1.08333…+360n,θ=180-1.08333…+360n