What is the general solution for (sin(a))/(50)=(sin(25))/(35) ?

The general solution for (sin(a))/(50)=(sin(25))/(35) is a=0.64818…+360n,a=180-0.64818…+360n

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(sin(a))/(50)=(sin(25))/(35)

\frac{sin ( a )}{50} = \frac{sin ( 2 5 ^{\circ} )}{35}

a = 0.64818 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.64818 \dots + 36 0^{\circ} n

Radians

a = 0.64818 \dots + 2 πn, a = π - 0.64818 \dots + 2 πn

Solution steps

\frac{sin ( a )}{50} = \frac{sin ( 2 5 ^{\circ} )}{35}

Multiply both sides by

10

\frac{sin ( a )}{50} = \frac{sin ( 2 5 ^{\circ} )}{35}

Multiply both sides by

10

\frac{sin ( a )}{50} \cdot 10 = \frac{sin ( 2 5 ^{\circ} )}{35} \cdot 10

Simplify

\frac{sin ( a )}{50} \cdot 10 = \frac{sin ( 2 5 ^{\circ} )}{35} \cdot 10

Simplify

\frac{sin ( a )}{50} \cdot 10 : \frac{sin ( a )}{5}

\frac{sin ( a )}{50} \cdot 10

Multiply fractions:

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

= \frac{sin ( a ) \cdot 10}{50}

Cancel the common factor:

10

= \frac{sin ( a )}{5}

Simplify

\frac{sin ( 2 5 ^{\circ} )}{35} \cdot 10 : \frac{2 sin ( 2 5 ^{\circ} )}{7}

\frac{sin ( 2 5 ^{\circ} )}{35} \cdot 10

Multiply fractions:

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

= \frac{sin ( 2 5 ^{\circ} ) \cdot 10}{35}

Cancel the common factor:

5

= \frac{2 sin ( 2 5 ^{\circ} )}{7}

\frac{sin ( a )}{5} = \frac{2 sin ( 2 5 ^{\circ} )}{7}

\frac{sin ( a )}{5} = \frac{2 sin ( 2 5 ^{\circ} )}{7}

\frac{sin ( a )}{5} = \frac{2 sin ( 2 5 ^{\circ} )}{7}

Multiply both sides by

5

\frac{sin ( a )}{5} = \frac{2 sin ( 2 5 ^{\circ} )}{7}

Multiply both sides by

5

\frac{5 sin ( a )}{5} = \frac{5 \cdot 2 sin ( 2 5 ^{\circ} )}{7}

Simplify

\frac{5 sin ( a )}{5} = \frac{5 \cdot 2 sin ( 2 5 ^{\circ} )}{7}

Simplify

\frac{5 sin ( a )}{5} : sin (a)

\frac{5 sin ( a )}{5}

Divide the numbers:

\frac{5}{5} = 1

= sin (a)

Simplify

\frac{5 \cdot 2 sin ( 2 5 ^{\circ} )}{7} : \frac{10 sin ( 2 5 ^{\circ} )}{7}

\frac{5 \cdot 2 sin ( 2 5 ^{\circ} )}{7}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10 sin ( 2 5 ^{\circ} )}{7}

sin (a) = \frac{10 sin ( 2 5 ^{\circ} )}{7}

sin (a) = \frac{10 sin ( 2 5 ^{\circ} )}{7}

sin (a) = \frac{10 sin ( 2 5 ^{\circ} )}{7}

Apply trig inverse properties

sin (a) = \frac{10 sin ( 2 5 ^{\circ} )}{7}

General solutions for

sin (a) = \frac{10 sin ( 2 5 ^{\circ} )}{7}

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

a = arcsin (\frac{10 sin ( 2 5 ^{\circ} )}{7}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{10 sin ( 2 5 ^{\circ} )}{7}) + 36 0^{\circ} n

a = arcsin (\frac{10 sin ( 2 5 ^{\circ} )}{7}) + 36 0^{\circ} n, a = 18 0^{\circ} - arcsin (\frac{10 sin ( 2 5 ^{\circ} )}{7}) + 36 0^{\circ} n

Show solutions in decimal form

a = 0.64818 \dots + 36 0^{\circ} n, a = 18 0^{\circ} - 0.64818 \dots + 36 0^{\circ} n

What is the general solution for (sin(a))/(50)=(sin(25))/(35) ?
The general solution for (sin(a))/(50)=(sin(25))/(35) is a=0.64818…+360n,a=180-0.64818…+360n