What is the general solution for (sin(45))/(497.01)=(sin(x))/(450) ?

The general solution for (sin(45))/(497.01)=(sin(x))/(450) is x=0.69479…+360n,x=180-0.69479…+360n

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Popular Trigonometry >

(sin(45))/(497.01)=(sin(x))/(450)

Solution

\frac{sin ( 4 5 ^{\circ} )}{497.01} = \frac{sin ( x )}{450}

Solution

x = 0.69479 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.69479 \dots + 36 0^{\circ} n

Radians

x = 0.69479 \dots + 2 πn, x = π - 0.69479 \dots + 2 πn

Solution steps

\frac{sin ( 4 5 ^{\circ} )}{497.01} = \frac{sin ( x )}{450}

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{\frac{2}{2}}{497.01} = \frac{sin ( x )}{450}

Switch sides

\frac{sin ( x )}{450} = \frac{\frac{2}{2}}{497.01}

Multiply both sides by

10

\frac{sin ( x )}{450} = \frac{\frac{2}{2}}{497.01}

Multiply both sides by

10

\frac{sin ( x )}{450} \cdot 10 = \frac{\frac{2}{2}}{497.01} \cdot 10

Simplify

\frac{sin ( x )}{450} \cdot 10 = \frac{\frac{2}{2}}{497.01} \cdot 10

Simplify

\frac{sin ( x )}{450} \cdot 10 : \frac{sin ( x )}{45}

\frac{sin ( x )}{450} \cdot 10

Multiply fractions:

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

= \frac{sin ( x ) \cdot 10}{450}

Cancel the common factor:

10

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

Simplify

\frac{\frac{2}{2}}{497.01} \cdot 10 : \frac{10 2}{994.02}

\frac{\frac{2}{2}}{497.01} \cdot 10

\frac{\frac{2}{2}}{497.01} = \frac{2}{994.02}

\frac{\frac{2}{2}}{497.01}

Apply the fraction rule:

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

= \frac{2}{2 \cdot 497.01}

Multiply the numbers:

2 \cdot 497.01 = 994.02

= \frac{2}{994.02}

= 10 \cdot \frac{2}{994.02}

Multiply fractions:

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

= \frac{2 \cdot 10}{994.02}

\frac{sin ( x )}{45} = \frac{10 2}{994.02}

\frac{sin ( x )}{45} = \frac{10 2}{994.02}

\frac{sin ( x )}{45} = \frac{10 2}{994.02}

Multiply both sides by

45

\frac{sin ( x )}{45} = \frac{10 2}{994.02}

Multiply both sides by

45

\frac{45 sin ( x )}{45} = \frac{45 \cdot 10 2}{994.02}

Simplify

\frac{45 sin ( x )}{45} = \frac{45 \cdot 10 2}{994.02}

Simplify

\frac{45 sin ( x )}{45} : sin (x)

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

Divide the numbers:

\frac{45}{45} = 1

= sin (x)

Simplify

\frac{45 \cdot 10 2}{994.02} : 0.64022 \dots

\frac{45 \cdot 10 2}{994.02}

Multiply the numbers:

45 \cdot 10 = 450

= \frac{450 2}{994.02}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{450 \cdot 1.41421 \dots}{994.02}

Multiply the numbers:

450 \cdot 1.41421 \dots = 636.39610 \dots

= \frac{636.39610 \dots}{994.02}

Divide the numbers:

\frac{636.39610 \dots}{994.02} = 0.64022 \dots

= 0.64022 \dots

sin (x) = 0.64022 \dots

sin (x) = 0.64022 \dots

sin (x) = 0.64022 \dots

Apply trig inverse properties

sin (x) = 0.64022 \dots

General solutions for

sin (x) = 0.64022 \dots

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

x = arcsin (0.64022 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.64022 \dots) + 36 0^{\circ} n

x = arcsin (0.64022 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.64022 \dots) + 36 0^{\circ} n

Show solutions in decimal form

x = 0.69479 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.69479 \dots + 36 0^{\circ} n

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for (sin(45))/(497.01)=(sin(x))/(450) ?
The general solution for (sin(45))/(497.01)=(sin(x))/(450) is x=0.69479…+360n,x=180-0.69479…+360n