What is the general solution for (sin(y))/(80)=(sin(40))/(60) ?

The general solution for (sin(y))/(80)=(sin(40))/(60) is y=1.02951…+360n,y=180-1.02951…+360n

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(sin(y))/(80)=(sin(40))/(60)

\frac{sin ( y )}{80} = \frac{sin ( 4 0 ^{\circ} )}{60}

y = 1.02951 \dots + 36 0^{\circ} n, y = 18 0^{\circ} - 1.02951 \dots + 36 0^{\circ} n

Solution steps

\frac{sin ( y )}{80} = \frac{sin ( 4 0 ^{\circ} )}{60}

Multiply both sides by

10

\frac{sin ( y )}{8} = \frac{sin ( 4 0 ^{\circ} )}{6}

Multiply both sides by

8

sin (y) = \frac{4 sin ( 4 0 ^{\circ} )}{3}

Apply trig inverse properties

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

Show solutions in decimal form

y = 1.02951 \dots + 36 0^{\circ} n, y = 18 0^{\circ} - 1.02951 \dots + 36 0^{\circ} n

cos (w) = 0.75 sin (9 0^{\circ} - w)

csc (4 x) = 2

3 tan^{2} (x) = 2 sec^{2} (x) + 1, 0^{\circ} \leq x \leq 18 0^{\circ}

2 arctan (x e^{\frac{0}{2}}) = \frac{π}{2}

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

What is the general solution for (sin(y))/(80)=(sin(40))/(60) ?
The general solution for (sin(y))/(80)=(sin(40))/(60) is y=1.02951…+360n,y=180-1.02951…+360n