What is the general solution for (sin(b))/(300)=(sin(49))/(500) ?

The general solution for (sin(b))/(300)=(sin(49))/(500) is b=0.46993…+360n,b=180-0.46993…+360n

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(sin(b))/(300)=(sin(49))/(500)

\frac{sin ( b )}{300} = \frac{sin ( 4 9 ^{\circ} )}{500}

b = 0.46993 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.46993 \dots + 36 0^{\circ} n

Radians

b = 0.46993 \dots + 2 πn, b = π - 0.46993 \dots + 2 πn

Solution steps

\frac{sin ( b )}{300} = \frac{sin ( 4 9 ^{\circ} )}{500}

Multiply both sides by

100

\frac{sin ( b )}{300} = \frac{sin ( 4 9 ^{\circ} )}{500}

Multiply both sides by

100

\frac{sin ( b )}{300} \cdot 100 = \frac{sin ( 4 9 ^{\circ} )}{500} \cdot 100

Simplify

\frac{sin ( b )}{300} \cdot 100 = \frac{sin ( 4 9 ^{\circ} )}{500} \cdot 100

Simplify

\frac{sin ( b )}{300} \cdot 100 : \frac{sin ( b )}{3}

\frac{sin ( b )}{300} \cdot 100

Multiply fractions:

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

= \frac{sin ( b ) \cdot 100}{300}

Cancel the common factor:

100

= \frac{sin ( b )}{3}

Simplify

\frac{sin ( 4 9 ^{\circ} )}{500} \cdot 100 : \frac{sin ( 4 9 ^{\circ} )}{5}

\frac{sin ( 4 9 ^{\circ} )}{500} \cdot 100

Multiply fractions:

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

= \frac{sin ( 4 9 ^{\circ} ) \cdot 100}{500}

Cancel the common factor:

100

= \frac{sin ( 4 9 ^{\circ} )}{5}

\frac{sin ( b )}{3} = \frac{sin ( 4 9 ^{\circ} )}{5}

\frac{sin ( b )}{3} = \frac{sin ( 4 9 ^{\circ} )}{5}

\frac{sin ( b )}{3} = \frac{sin ( 4 9 ^{\circ} )}{5}

Multiply both sides by

3

\frac{sin ( b )}{3} = \frac{sin ( 4 9 ^{\circ} )}{5}

Multiply both sides by

3

\frac{3 sin ( b )}{3} = \frac{3 sin ( 4 9 ^{\circ} )}{5}

Simplify

sin (b) = \frac{3 sin ( 4 9 ^{\circ} )}{5}

sin (b) = \frac{3 sin ( 4 9 ^{\circ} )}{5}

Apply trig inverse properties

sin (b) = \frac{3 sin ( 4 9 ^{\circ} )}{5}

General solutions for

sin (b) = \frac{3 sin ( 4 9 ^{\circ} )}{5}

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

b = arcsin (\frac{3 sin ( 4 9 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{3 sin ( 4 9 ^{\circ} )}{5}) + 36 0^{\circ} n

b = arcsin (\frac{3 sin ( 4 9 ^{\circ} )}{5}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{3 sin ( 4 9 ^{\circ} )}{5}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.46993 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.46993 \dots + 36 0^{\circ} n

sin (θ) = cos (2 θ + 6 0^{\circ})

tan (θ) = \frac{- 12}{5}

\frac{1 + tan ( \frac{x}{2} )}{1 - tan ( \frac{x}{2} )} = 4.137131

cos (θ) = 0.51

csc (θ) = \frac{- 2 3}{3}

What is the general solution for (sin(b))/(300)=(sin(49))/(500) ?
The general solution for (sin(b))/(300)=(sin(49))/(500) is b=0.46993…+360n,b=180-0.46993…+360n