What is the general solution for 15sin(30)=10sin(x) ?

The general solution for 15sin(30)=10sin(x) is x=0.84806…+360n,x=180-0.84806…+360n

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15sin(30)=10sin(x)

15 sin (3 0^{\circ}) = 10 sin (x)

x = 0.84806 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.84806 \dots + 36 0^{\circ} n

Solution steps

15 sin (3 0^{\circ}) = 10 sin (x)

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

15 \cdot \frac{1}{2} = 10 sin (x)

Switch sides

10 sin (x) = 15 \cdot \frac{1}{2}

Divide both sides by

10

sin (x) = \frac{3}{4}

Apply trig inverse properties

x = arcsin (\frac{3}{4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{4}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.84806 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.84806 \dots + 36 0^{\circ} n

sin (0) = - sin (o) cos (0)

\frac{sin ( 78.0538888 9 ^{\circ} )}{8} = \frac{sin ( x )}{10}

sin (x) = 32

88.2 sin (x) - 12.78 = 0.1 \cdot 88.2 cos (x)

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

What is the general solution for 15sin(30)=10sin(x) ?
The general solution for 15sin(30)=10sin(x) is x=0.84806…+360n,x=180-0.84806…+360n