What is the general solution for (sin(x))/(700)=(sin(45))/(497) ?

The general solution for (sin(x))/(700)=(sin(45))/(497) is x=1.48048…+360n,x=180-1.48048…+360n

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Popular Trigonometry >

(sin(x))/(700)=(sin(45))/(497)

Solution

\frac{sin ( x )}{700} = \frac{sin ( 4 5 ^{\circ} )}{497}

Solution

x = 1.48048 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.48048 \dots + 36 0^{\circ} n

Radians

x = 1.48048 \dots + 2 πn, x = π - 1.48048 \dots + 2 πn

Solution steps

\frac{sin ( x )}{700} = \frac{sin ( 4 5 ^{\circ} )}{497}

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

= \frac{2}{2}

\frac{sin ( x )}{700} = \frac{\frac{2}{2}}{497}

Multiply both sides by

100

\frac{sin ( x )}{700} = \frac{\frac{2}{2}}{497}

Multiply both sides by

100

\frac{sin ( x )}{700} \cdot 100 = \frac{\frac{2}{2}}{497} \cdot 100

Simplify

\frac{sin ( x )}{700} \cdot 100 = \frac{\frac{2}{2}}{497} \cdot 100

Simplify

\frac{sin ( x )}{700} \cdot 100 : \frac{sin ( x )}{7}

\frac{sin ( x )}{700} \cdot 100

Multiply fractions:

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

= \frac{sin ( x ) \cdot 100}{700}

Cancel the common factor:

100

= \frac{sin ( x )}{7}

Simplify

\frac{\frac{2}{2}}{497} \cdot 100 : \frac{50 2}{497}

\frac{\frac{2}{2}}{497} \cdot 100

\frac{\frac{2}{2}}{497} = \frac{2}{994}

\frac{\frac{2}{2}}{497}

Apply the fraction rule:

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

= \frac{2}{2 \cdot 497}

Multiply the numbers:

2 \cdot 497 = 994

= \frac{2}{994}

= 100 \cdot \frac{2}{994}

Multiply fractions:

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

= \frac{2 \cdot 100}{994}

Cancel the common factor:

2

= \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

Multiply both sides by

7

\frac{sin ( x )}{7} = \frac{50 2}{497}

Multiply both sides by

7

\frac{7 sin ( x )}{7} = \frac{7 \cdot 50 2}{497}

Simplify

\frac{7 sin ( x )}{7} = \frac{7 \cdot 50 2}{497}

Simplify

\frac{7 sin ( x )}{7} : sin (x)

\frac{7 sin ( x )}{7}

Divide the numbers:

\frac{7}{7} = 1

= sin (x)

Simplify

\frac{7 \cdot 50 2}{497} : \frac{50 2}{71}

\frac{7 \cdot 50 2}{497}

Multiply the numbers:

7 \cdot 50 = 350

= \frac{350 2}{497}

Cancel the common factor:

7

= \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

Apply trig inverse properties

sin (x) = \frac{50 2}{71}

General solutions for

sin (x) = \frac{50 2}{71}

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

x = arcsin (\frac{50 2}{71}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{50 2}{71}) + 36 0^{\circ} n

x = arcsin (\frac{50 2}{71}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{50 2}{71}) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.48048 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.48048 \dots + 36 0^{\circ} n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for (sin(x))/(700)=(sin(45))/(497) ?
The general solution for (sin(x))/(700)=(sin(45))/(497) is x=1.48048…+360n,x=180-1.48048…+360n