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

Radians

θ = 0.24344 \dots + 2 πk, θ = π - 0.24344 \dots + 2 πk

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

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

Multiply both sides by

3 in

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

Simplify

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

Simplify

\frac{sin ( θ ) \cdot 3 in}{3 in} : sin (θ)

\frac{sin ( θ ) \cdot 3 in}{3 in}

Divide the numbers:

\frac{3}{3} = 1

= \frac{in sin ( θ )}{in}

Cancel the common factor:

i

= \frac{n sin ( θ )}{n}

Cancel the common factor:

n

= sin (θ)

Simplify

\frac{sin ( 4 0 ^{\circ} ) \cdot 3 in}{8 in} : \frac{3 sin ( 4 0 ^{\circ} )}{8}

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

Cancel the common factor:

i

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

Cancel the common factor:

n

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

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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