What is the general solution for (sin(150))/(500)=(sin(x))/(45) ?

The general solution for (sin(150))/(500)=(sin(x))/(45) is x=0.04501…+360n,x=180-0.04501…+360n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(sin(150))/(500)=(sin(x))/(45)

Solution

\frac{sin ( 15 0 ^{\circ} )}{500} = \frac{sin ( x )}{45}

Solution

x = 0.04501 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.04501 \dots + 36 0^{\circ} n

Radians

x = 0.04501 \dots + 2 πn, x = π - 0.04501 \dots + 2 πn

Solution steps

\frac{sin ( 15 0 ^{\circ} )}{500} = \frac{sin ( x )}{45}

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\circ})

Use the following trivial identity:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

\frac{\frac{1}{2}}{500} = \frac{sin ( x )}{45}

Switch sides

\frac{sin ( x )}{45} = \frac{\frac{1}{2}}{500}

Multiply both sides by

100

\frac{sin ( x )}{45} = \frac{\frac{1}{2}}{500}

Multiply both sides by

100

\frac{sin ( x )}{45} \cdot 100 = \frac{\frac{1}{2}}{500} \cdot 100

Simplify

\frac{sin ( x )}{45} \cdot 100 = \frac{\frac{1}{2}}{500} \cdot 100

Simplify

\frac{sin ( x )}{45} \cdot 100 : \frac{20 sin ( x )}{9}

\frac{sin ( x )}{45} \cdot 100

Multiply fractions:

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

= \frac{sin ( x ) \cdot 100}{45}

Cancel the common factor:

5

= \frac{20 sin ( x )}{9}

Simplify

\frac{\frac{1}{2}}{500} \cdot 100 : \frac{1}{10}

\frac{\frac{1}{2}}{500} \cdot 100

\frac{\frac{1}{2}}{500} = \frac{1}{1000}

\frac{\frac{1}{2}}{500}

Apply the fraction rule:

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

= \frac{1}{2 \cdot 500}

Multiply the numbers:

2 \cdot 500 = 1000

= \frac{1}{1000}

= 100 \cdot \frac{1}{1000}

Multiply fractions:

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

= \frac{1 \cdot 100}{1000}

Multiply the numbers:

1 \cdot 100 = 100

= \frac{100}{1000}

Cancel the common factor:

100

= \frac{1}{10}

\frac{20 sin ( x )}{9} = \frac{1}{10}

\frac{20 sin ( x )}{9} = \frac{1}{10}

\frac{20 sin ( x )}{9} = \frac{1}{10}

Multiply both sides by

9

\frac{20 sin ( x )}{9} = \frac{1}{10}

Multiply both sides by

9

\frac{9 \cdot 20 sin ( x )}{9} = \frac{1 \cdot 9}{10}

Simplify

\frac{9 \cdot 20 sin ( x )}{9} = \frac{1 \cdot 9}{10}

Simplify

\frac{9 \cdot 20 sin ( x )}{9} : 20 sin (x)

\frac{9 \cdot 20 sin ( x )}{9}

Multiply the numbers:

9 \cdot 20 = 180

= \frac{180 sin ( x )}{9}

Divide the numbers:

\frac{180}{9} = 20

= 20 sin (x)

Simplify

\frac{1 \cdot 9}{10} : \frac{9}{10}

\frac{1 \cdot 9}{10}

Multiply the numbers:

1 \cdot 9 = 9

= \frac{9}{10}

20 sin (x) = \frac{9}{10}

20 sin (x) = \frac{9}{10}

20 sin (x) = \frac{9}{10}

Divide both sides by

20

20 sin (x) = \frac{9}{10}

Divide both sides by

20

\frac{20 sin ( x )}{20} = \frac{\frac{9}{10}}{20}

Simplify

\frac{20 sin ( x )}{20} = \frac{\frac{9}{10}}{20}

Simplify

\frac{20 sin ( x )}{20} : sin (x)

\frac{20 sin ( x )}{20}

Divide the numbers:

\frac{20}{20} = 1

= sin (x)

Simplify

\frac{\frac{9}{10}}{20} : \frac{9}{200}

\frac{\frac{9}{10}}{20}

Apply the fraction rule:

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

= \frac{9}{10 \cdot 20}

Multiply the numbers:

10 \cdot 20 = 200

= \frac{9}{200}

sin (x) = \frac{9}{200}

sin (x) = \frac{9}{200}

sin (x) = \frac{9}{200}

Apply trig inverse properties

sin (x) = \frac{9}{200}

General solutions for

sin (x) = \frac{9}{200}

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

x = arcsin (\frac{9}{200}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9}{200}) + 36 0^{\circ} n

x = arcsin (\frac{9}{200}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{9}{200}) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.04501 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.04501 \dots + 36 0^{\circ} n

Popular Examples

sec(x)-tan(x)=2

sec (x) - tan (x) = 2

sin((2pi(t+101.75))/(365))=-1

sin (\frac{2 π ( t + 101.75 )}{365}) = - 1

2sin^2(θ)-2=cos^2(θ),0<= θ<= 2pi

2 sin^{2} (θ) - 2 = cos^{2} (θ), 0 \leq θ \leq 2 π

cos(θ)=-(sqrt(7))/5

cos (θ) = - \frac{7}{5}

sin(pi+x)=sin(x)

sin (π + x) = sin (x)

Frequently Asked Questions (FAQ)

What is the general solution for (sin(150))/(500)=(sin(x))/(45) ?
The general solution for (sin(150))/(500)=(sin(x))/(45) is x=0.04501…+360n,x=180-0.04501…+360n