What is the general solution for (sin(150))/(500)=(sin(x))/(45) ?

The general solution for (sin(150))/(500)=(sin(x))/(45) is x=0.04501…+360n,x=180-0.04501…+360n

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(sin(150))/(500)=(sin(x))/(45)

\frac{sin ( 15 0 ^{\circ} )}{500} = \frac{sin ( x )}{45}

x = 0.04501 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.04501 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( 15 0 ^{\circ} )}{500} = \frac{sin ( x )}{45}

sin (15 0^{\circ}) = \frac{1}{2}

\frac{\frac{1}{2}}{500} = \frac{sin ( x )}{45}

Switch sides

\frac{sin ( x )}{45} = \frac{\frac{1}{2}}{500}

Multiply both sides by

100

\frac{20 sin ( x )}{9} = \frac{1}{10}

Multiply both sides by

9

20 sin (x) = \frac{9}{10}

Divide both sides by

20

sin (x) = \frac{9}{200}

Apply trig inverse properties

x = arcsin (\frac{9}{200}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9}{200}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.04501 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.04501 \dots + 36 0^{\circ} n

sec (x) - tan (x) = 2

sin (\frac{2 π ( t + 101.75 )}{365}) = - 1

2 sin^{2} (θ) - 2 = cos^{2} (θ), 0 \leq θ \leq 2 π

cos (θ) = - \frac{7}{5}

sin (π + x) = sin (x)

What is the general solution for (sin(150))/(500)=(sin(x))/(45) ?
The general solution for (sin(150))/(500)=(sin(x))/(45) is x=0.04501…+360n,x=180-0.04501…+360n