What is the general solution for (sin(θ))/(1.3)=(sin(125))/(2.8519) ?

The general solution for (sin(θ))/(1.3)=(sin(125))/(2.8519) is θ=0.38267…+360n,θ=180-0.38267…+360n

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(sin(θ))/(1.3)=(sin(125))/(2.8519)

\frac{sin ( θ )}{1.3} = \frac{sin ( 12 5 ^{\circ} )}{2.8519}

θ = 0.38267 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.38267 \dots + 36 0^{\circ} n

Radians

θ = 0.38267 \dots + 2 πn, θ = π - 0.38267 \dots + 2 πn

Solution steps

\frac{sin ( θ )}{1.3} = \frac{sin ( 12 5 ^{\circ} )}{2.8519}

Multiply both sides by

1.3

\frac{sin ( θ )}{1.3} = \frac{sin ( 12 5 ^{\circ} )}{2.8519}

Multiply both sides by

1.3

\frac{1.3 sin ( θ )}{1.3} = \frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}

Simplify

sin (θ) = \frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}

sin (θ) = \frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}

Apply trig inverse properties

sin (θ) = \frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}

General solutions for

sin (θ) = \frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}

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

θ = arcsin (\frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}) + 36 0^{\circ} n

θ = arcsin (\frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{1.3 sin ( 12 5 ^{\circ} )}{2.8519}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.38267 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.38267 \dots + 36 0^{\circ} n

cot^{2} (θ) = \frac{1}{3}

x, y^{3} - sin^{2} (x) = 1

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

sec (θ) - 2 cos (θ) = 0

sin (θ) = \frac{1}{2}, 0 \leq θ \leq 4 π

What is the general solution for (sin(θ))/(1.3)=(sin(125))/(2.8519) ?
The general solution for (sin(θ))/(1.3)=(sin(125))/(2.8519) is θ=0.38267…+360n,θ=180-0.38267…+360n