What is the general solution for (sin(115))/(20)=(sin(b))/(11) ?

The general solution for (sin(115))/(20)=(sin(b))/(11) is b=0.52183…+360n,b=180-0.52183…+360n

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Popular Trigonometry >

(sin(115))/(20)=(sin(b))/(11)

Solution

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

Solution

b = 0.52183 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.52183 \dots + 36 0^{\circ} n

Radians

b = 0.52183 \dots + 2 πn, b = π - 0.52183 \dots + 2 πn

Solution steps

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

Switch sides

\frac{sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{20}

Multiply both sides by

10

\frac{sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{20}

Multiply both sides by

10

\frac{sin ( b )}{11} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Simplify

\frac{sin ( b )}{11} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Simplify

\frac{sin ( b )}{11} \cdot 10 : \frac{10 sin ( b )}{11}

\frac{sin ( b )}{11} \cdot 10

Multiply fractions:

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

= \frac{sin ( b ) \cdot 10}{11}

Simplify

\frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10 : \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

Multiply fractions:

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

= \frac{sin ( 11 5 ^{\circ} ) \cdot 10}{20}

Cancel the common factor:

10

= \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

Multiply both sides by

11

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

Multiply both sides by

11

\frac{11 \cdot 10 sin ( b )}{11} = \frac{11 sin ( 11 5 ^{\circ} )}{2}

Simplify

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

Divide both sides by

10

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

Divide both sides by

10

\frac{10 sin ( b )}{10} = \frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

Simplify

\frac{10 sin ( b )}{10} = \frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

Simplify

\frac{10 sin ( b )}{10} : sin (b)

\frac{10 sin ( b )}{10}

Divide the numbers:

\frac{10}{10} = 1

= sin (b)

Simplify

\frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10} : \frac{11 sin ( 11 5 ^{\circ} )}{20}

\frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

Apply the fraction rule:

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

= \frac{11 sin ( 11 5 ^{\circ} )}{2 \cdot 10}

Multiply the numbers:

2 \cdot 10 = 20

= \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

Apply trig inverse properties

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

General solutions for

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

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

b = arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n

b = arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n

Show solutions in decimal form

b = 0.52183 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.52183 \dots + 36 0^{\circ} n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for (sin(115))/(20)=(sin(b))/(11) ?
The general solution for (sin(115))/(20)=(sin(b))/(11) is b=0.52183…+360n,b=180-0.52183…+360n