What is the general solution for 1*sin(45)=1.57*sin(θ) ?

The general solution for 1*sin(45)=1.57*sin(θ) is θ=0.46719…+360n,θ=180-0.46719…+360n

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1sin(45)=1.57sin(θ)

1 \cdot 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

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

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

1 \cdot \frac{2}{2} = 1.57 sin (θ)

Switch sides

1.57 sin (θ) = 1 \cdot \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{sin ( x )}{2 - 2 sin ^{2} ( x )} = 0

tan (θ) = 3, 0 \leq θ < 2 π

0 = - cos (8 x) + cos (2 x)

3 cos^{2} (x) + cos (x) - 2 = 0, 0 \leq x \leq 2 π

- 1 = tan^{2} (θ)

What is the general solution for 1*sin(45)=1.57*sin(θ) ?
The general solution for 1*sin(45)=1.57*sin(θ) is θ=0.46719…+360n,θ=180-0.46719…+360n