What is the general solution for (sin(x))/(45)=(sin(35))/(30) ?

The general solution for (sin(x))/(45)=(sin(35))/(30) is x=1.03598…+360n,x=180-1.03598…+360n

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(sin(x))/(45)=(sin(35))/(30)

\frac{sin ( x )}{45} = \frac{sin ( 3 5 ^{\circ} )}{30}

x = 1.03598 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.03598 \dots + 36 0^{\circ} n

Radians

x = 1.03598 \dots + 2 πn, x = π - 1.03598 \dots + 2 πn

Solution steps

\frac{sin ( x )}{45} = \frac{sin ( 3 5 ^{\circ} )}{30}

Multiply both sides by

10

\frac{sin ( x )}{45} = \frac{sin ( 3 5 ^{\circ} )}{30}

Multiply both sides by

10

\frac{sin ( x )}{45} \cdot 10 = \frac{sin ( 3 5 ^{\circ} )}{30} \cdot 10

Simplify

\frac{sin ( x )}{45} \cdot 10 = \frac{sin ( 3 5 ^{\circ} )}{30} \cdot 10

Simplify

\frac{sin ( x )}{45} \cdot 10 : \frac{2 sin ( x )}{9}

\frac{sin ( x )}{45} \cdot 10

Multiply fractions:

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

= \frac{sin ( x ) \cdot 10}{45}

Cancel the common factor:

5

= \frac{2 sin ( x )}{9}

Simplify

\frac{sin ( 3 5 ^{\circ} )}{30} \cdot 10 : \frac{sin ( 3 5 ^{\circ} )}{3}

\frac{sin ( 3 5 ^{\circ} )}{30} \cdot 10

Multiply fractions:

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

= \frac{sin ( 3 5 ^{\circ} ) \cdot 10}{30}

Cancel the common factor:

10

= \frac{sin ( 3 5 ^{\circ} )}{3}

\frac{2 sin ( x )}{9} = \frac{sin ( 3 5 ^{\circ} )}{3}

\frac{2 sin ( x )}{9} = \frac{sin ( 3 5 ^{\circ} )}{3}

\frac{2 sin ( x )}{9} = \frac{sin ( 3 5 ^{\circ} )}{3}

Multiply both sides by

9

\frac{2 sin ( x )}{9} = \frac{sin ( 3 5 ^{\circ} )}{3}

Multiply both sides by

9

\frac{9 \cdot 2 sin ( x )}{9} = \frac{9 sin ( 3 5 ^{\circ} )}{3}

Simplify

2 sin (x) = 3 sin (3 5^{\circ})

2 sin (x) = 3 sin (3 5^{\circ})

Divide both sides by

2

2 sin (x) = 3 sin (3 5^{\circ})

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{3 sin ( 3 5 ^{\circ} )}{2}

Simplify

sin (x) = \frac{3 sin ( 3 5 ^{\circ} )}{2}

sin (x) = \frac{3 sin ( 3 5 ^{\circ} )}{2}

Apply trig inverse properties

sin (x) = \frac{3 sin ( 3 5 ^{\circ} )}{2}

General solutions for

sin (x) = \frac{3 sin ( 3 5 ^{\circ} )}{2}

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

x = arcsin (\frac{3 sin ( 3 5 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 5 ^{\circ} )}{2}) + 36 0^{\circ} n

x = arcsin (\frac{3 sin ( 3 5 ^{\circ} )}{2}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3 sin ( 3 5 ^{\circ} )}{2}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.03598 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.03598 \dots + 36 0^{\circ} n

cos (x) = \frac{4 ( - \frac{1}{2} ) - 1}{3}

1 = l sin (x), 2 = l cos (x)

y, t = 2 cot (6 0^{\circ} y + 3 0^{\circ})

sec (y) = - 2

- 1 + 2 sin^{2} (x) = 0

What is the general solution for (sin(x))/(45)=(sin(35))/(30) ?
The general solution for (sin(x))/(45)=(sin(35))/(30) is x=1.03598…+360n,x=180-1.03598…+360n