What is the general solution for 50sin(45)=600sin(θ) ?

The general solution for 50sin(45)=600sin(θ) is θ=0.05895…+360n,θ=180-0.05895…+360n

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50sin(45)=600sin(θ)

50 sin (4 5^{\circ}) = 600 sin (θ)

θ = 0.05895 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.05895 \dots + 36 0^{\circ} n

Solution steps

50 sin (4 5^{\circ}) = 600 sin (θ)

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

50 \cdot \frac{2}{2} = 600 sin (θ)

Switch sides

600 sin (θ) = 50 \cdot \frac{2}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

600 sin (θ) = \frac{2 \cdot 50}{2}

Divide the numbers:

\frac{50}{2} = 25

600 sin (θ) = 252

Divide both sides by

600

sin (θ) = \frac{2}{24}

Apply trig inverse properties

θ = arcsin (\frac{2}{24}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{2}{24}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.05895 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.05895 \dots + 36 0^{\circ} n

a, tan (a \cdot x^{0.5}) = - x^{0.5}

sin (x) = 35, csc (x)

2 + 2 cos (x) = \frac{2}{1 + cos ( x )}

cos^{2} (θ) + 0.339 cos (θ) - 1 = 0

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

What is the general solution for 50sin(45)=600sin(θ) ?
The general solution for 50sin(45)=600sin(θ) is θ=0.05895…+360n,θ=180-0.05895…+360n