What is the general solution for 1.74*sin(40.31)=1.33*sin(θ) ?

The general solution for 1.74*sin(40.31)=1.33*sin(θ) is θ=1.00909…+360n,θ=180-1.00909…+360n

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1.74sin(40.31)=1.33sin(θ)

1.74 \cdot sin (40.3 1^{\circ}) = 1.33 \cdot sin (θ)

θ = 1.00909 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 1.00909 \dots + 36 0^{\circ} n

Radians

θ = 1.00909 \dots + 2 πn, θ = π - 1.00909 \dots + 2 πn

Solution steps

1.74 sin (40.3 1^{\circ}) = 1.33 sin (θ)

Switch sides

1.33 sin (θ) = 1.74 sin (40.30999 \dots^{\circ})

Divide both sides by

1.33

1.33 sin (θ) = 1.74 sin (40.30999 \dots^{\circ})

Divide both sides by

1.33

\frac{1.33 sin ( θ )}{1.33} = \frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}

Simplify

sin (θ) = \frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}

sin (θ) = \frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}

Apply trig inverse properties

sin (θ) = \frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}

General solutions for

sin (θ) = \frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}

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

θ = arcsin (\frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}) + 36 0^{\circ} n

θ = arcsin (\frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{1.74 sin ( 40.30999 \dots ^{\circ} )}{1.33}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 1.00909 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 1.00909 \dots + 36 0^{\circ} n

5 sin (θ) = 5 cos (θ)

θ, 2 cos (θ) = sin (θ) + cos (θ)

x, cos (x + y) + sin (x) = 0

2 sin (x - \frac{π}{4}) + 1 = 2

3 (tan (x) - 2) = 2 tan (- 7)

What is the general solution for 1.74*sin(40.31)=1.33*sin(θ) ?
The general solution for 1.74*sin(40.31)=1.33*sin(θ) is θ=1.00909…+360n,θ=180-1.00909…+360n