What is the general solution for (sin(x))/(37)=(sin(30))/(30) ?

The general solution for (sin(x))/(37)=(sin(30))/(30) is x=0.66450…+360n,x=180-0.66450…+360n

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(sin(x))/(37)=(sin(30))/(30)

\frac{sin ( x )}{37} = \frac{sin ( 3 0 ^{\circ} )}{30}

x = 0.66450 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.66450 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( x )}{37} = \frac{sin ( 3 0 ^{\circ} )}{30}

sin (3 0^{\circ}) = \frac{1}{2}

\frac{sin ( x )}{37} = \frac{\frac{1}{2}}{30}

Multiply both sides by

10

\frac{10 sin ( x )}{37} = \frac{1}{6}

Multiply both sides by

37

10 sin (x) = \frac{37}{6}

Divide both sides by

10

sin (x) = \frac{37}{60}

Apply trig inverse properties

x = arcsin (\frac{37}{60}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{37}{60}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.66450 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.66450 \dots + 36 0^{\circ} n

1 - cos (x) = cos (x)

sin^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

2 cos^{3} (θ) = cos (θ)

t, x = arccos (\frac{1}{1 + t ^{2}})

sin (x) \cdot cos (x) = sin (2 x)

What is the general solution for (sin(x))/(37)=(sin(30))/(30) ?
The general solution for (sin(x))/(37)=(sin(30))/(30) is x=0.66450…+360n,x=180-0.66450…+360n