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

Radians

θ = 0.05895 \dots + 2 πn, θ = π - 0.05895 \dots + 2 πn

Solution steps

50 sin (4 5^{\circ}) = 600 sin (θ)

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

sin (4 5^{\circ})

Use the following trivial identity:

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

sin (4 5^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \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

600 sin (θ) = 252

Divide both sides by

600

\frac{600 sin ( θ )}{600} = \frac{25 2}{600}

Simplify

sin (θ) = \frac{2}{24}

sin (θ) = \frac{2}{24}

Apply trig inverse properties

sin (θ) = \frac{2}{24}

General solutions for

sin (θ) = \frac{2}{24}

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

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

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

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

k sin (x) - c = 0

cos (x) = sin (x - \frac{π}{2})

5 cos (x) + 2 = 0, 0 \leq x \leq 2 π

2 sin (x) cos (x) - sin (2 x) cos (2 x) = 0

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