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

10 sin (x) + 4 = 10

4. 3^{2} = 3. 8^{2} + 6. 3^{2} + 2 (3.8) (6.3) cos (b)

cos^{2} (x) - 4 cos (x) + 4 = 0

t, x - 4 = sec^{2} (t)

csc (θ) = \frac{34}{3}, cos (θ) > 0

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