What is the general solution for sin(45)=1.57*sin(θ) ?

The general solution for sin(45)=1.57*sin(θ) is θ=0.46719…+360n,θ=180-0.46719…+360n

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sin(45)=1.57*sin(θ)

sin (4 5^{\circ}) = 1.57 \cdot sin (θ)

θ = 0.46719 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.46719 \dots + 36 0^{\circ} n

Solution steps

sin (4 5^{\circ}) = 1.57 sin (θ)

sin (4 5^{\circ}) = \frac{2}{2}

\frac{2}{2} = 1.57 sin (θ)

Switch sides

1.57 sin (θ) = \frac{2}{2}

Multiply both sides by

100

157 sin (θ) = 502

Divide both sides by

157

sin (θ) = \frac{50 2}{157}

Apply trig inverse properties

θ = arcsin (\frac{50 2}{157}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{50 2}{157}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.46719 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.46719 \dots + 36 0^{\circ} n

\frac{2}{3} = sec (x)

3 (cos (x) - 1) = - 1

9.6 8^{2} = 12. 5^{2} + 6.4 7^{2} - 2 \cdot 12.5 \cdot 6.47 \cdot cos (θ)

- 4 = \frac{sin ( θ )}{cos ( θ )}

3 = cos (θ)

What is the general solution for sin(45)=1.57*sin(θ) ?
The general solution for sin(45)=1.57*sin(θ) is θ=0.46719…+360n,θ=180-0.46719…+360n