What is the general solution for (sin(40))/(8in)=(sin(θ))/(3in) ?

The general solution for (sin(40))/(8in)=(sin(θ))/(3in) is θ=0.24344…+360k,θ=180-0.24344…+360k

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(sin(40))/(8in)=(sin(θ))/(3in)

\frac{sin ( 4 0 ^{\circ} )}{8 in} = \frac{sin ( θ )}{3 in}

θ = 0.24344 \dots + 36 0^{\circ} k, θ = 18 0^{\circ} - 0.24344 \dots + 36 0^{\circ} k

Solution steps

\frac{sin ( 4 0 ^{\circ} )}{8 in} = \frac{sin ( θ )}{3 in}

Switch sides

\frac{sin ( θ )}{3 in} = \frac{sin ( 4 0 ^{\circ} )}{8 in}

Multiply both sides by

3 in

sin (θ) = \frac{3 sin ( 4 0 ^{\circ} )}{8}; 3 in \neq = 0

Apply trig inverse properties

θ = arcsin (\frac{3 sin ( 4 0 ^{\circ} )}{8}) + 36 0^{\circ} k, θ = 18 0^{\circ} - arcsin (\frac{3 sin ( 4 0 ^{\circ} )}{8}) + 36 0^{\circ} k

Show solutions in decimal form

θ = 0.24344 \dots + 36 0^{\circ} k, θ = 18 0^{\circ} - 0.24344 \dots + 36 0^{\circ} k

cos (θ) = 0.925

cot (θ) = - \frac{3}{8}

1 - sin (t) = 0

θ, 6 = ρ sin (φ) sin (θ)

tan^{2} (θ) sec^{2} (θ) = 3

What is the general solution for (sin(40))/(8in)=(sin(θ))/(3in) ?
The general solution for (sin(40))/(8in)=(sin(θ))/(3in) is θ=0.24344…+360k,θ=180-0.24344…+360k