What is the general solution for (sin(50))/(10)=(sin(q))/(12) ?

The general solution for (sin(50))/(10)=(sin(q))/(12) is q=1.16617…+360n,q=180-1.16617…+360n

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(sin(50))/(10)=(sin(q))/(12)

\frac{sin ( 5 0 ^{\circ} )}{10} = \frac{sin ( q )}{12}

q = 1.16617 \dots + 36 0^{\circ} n, q = 18 0^{\circ} - 1.16617 \dots + 36 0^{\circ} n

Radians

q = 1.16617 \dots + 2 πn, q = π - 1.16617 \dots + 2 πn

Solution steps

\frac{sin ( 5 0 ^{\circ} )}{10} = \frac{sin ( q )}{12}

Switch sides

\frac{sin ( q )}{12} = \frac{sin ( 5 0 ^{\circ} )}{10}

Multiply both sides by

10

\frac{sin ( q )}{12} = \frac{sin ( 5 0 ^{\circ} )}{10}

Multiply both sides by

10

\frac{sin ( q )}{12} \cdot 10 = \frac{sin ( 5 0 ^{\circ} )}{10} \cdot 10

Simplify

\frac{sin ( q )}{12} \cdot 10 = \frac{sin ( 5 0 ^{\circ} )}{10} \cdot 10

Simplify

\frac{sin ( q )}{12} \cdot 10 : \frac{5 sin ( q )}{6}

\frac{sin ( q )}{12} \cdot 10

Multiply fractions:

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

= \frac{sin ( q ) \cdot 10}{12}

Cancel the common factor:

2

= \frac{5 sin ( q )}{6}

Simplify

\frac{sin ( 5 0 ^{\circ} )}{10} \cdot 10 : sin (5 0^{\circ})

\frac{sin ( 5 0 ^{\circ} )}{10} \cdot 10

Multiply fractions:

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

= \frac{sin ( 5 0 ^{\circ} ) \cdot 10}{10}

Cancel the common factor:

10

= sin (5 0^{\circ})

\frac{5 sin ( q )}{6} = sin (5 0^{\circ})

\frac{5 sin ( q )}{6} = sin (5 0^{\circ})

\frac{5 sin ( q )}{6} = sin (5 0^{\circ})

Multiply both sides by

6

\frac{5 sin ( q )}{6} = sin (5 0^{\circ})

Multiply both sides by

6

\frac{6 \cdot 5 sin ( q )}{6} = 6 sin (5 0^{\circ})

Simplify

5 sin (q) = 6 sin (5 0^{\circ})

5 sin (q) = 6 sin (5 0^{\circ})

Divide both sides by

5

5 sin (q) = 6 sin (5 0^{\circ})

Divide both sides by

5

\frac{5 sin ( q )}{5} = \frac{6 sin ( 5 0 ^{\circ} )}{5}

Simplify

sin (q) = \frac{6 sin ( 5 0 ^{\circ} )}{5}

sin (q) = \frac{6 sin ( 5 0 ^{\circ} )}{5}

Apply trig inverse properties

sin (q) = \frac{6 sin ( 5 0 ^{\circ} )}{5}

General solutions for

sin (q) = \frac{6 sin ( 5 0 ^{\circ} )}{5}

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

q = arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{5}) + 36 0^{\circ} n, q = 18 0^{\circ} - arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{5}) + 36 0^{\circ} n

q = arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{5}) + 36 0^{\circ} n, q = 18 0^{\circ} - arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

q = 1.16617 \dots + 36 0^{\circ} n, q = 18 0^{\circ} - 1.16617 \dots + 36 0^{\circ} n

What is the general solution for (sin(50))/(10)=(sin(q))/(12) ?
The general solution for (sin(50))/(10)=(sin(q))/(12) is q=1.16617…+360n,q=180-1.16617…+360n