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

Radians

y = 1.02951 \dots + 2 πn, y = π - 1.02951 \dots + 2 πn

Solution steps

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

Multiply both sides by

10

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

Multiply both sides by

10

\frac{sin ( y )}{80} \cdot 10 = \frac{sin ( 4 0 ^{\circ} )}{60} \cdot 10

Simplify

\frac{sin ( y )}{80} \cdot 10 = \frac{sin ( 4 0 ^{\circ} )}{60} \cdot 10

Simplify

\frac{sin ( y )}{80} \cdot 10 : \frac{sin ( y )}{8}

\frac{sin ( y )}{80} \cdot 10

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{sin ( y ) \cdot 10}{80}

Cancel the common factor:

10

= \frac{sin ( y )}{8}

Simplify

\frac{sin ( 4 0 ^{\circ} )}{60} \cdot 10 : \frac{sin ( 4 0 ^{\circ} )}{6}

\frac{sin ( 4 0 ^{\circ} )}{60} \cdot 10

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{sin ( 4 0 ^{\circ} ) \cdot 10}{60}

Cancel the common factor:

10

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

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

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

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

Multiply both sides by

8

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

Multiply both sides by

8

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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