What is the general solution for (sin(90))/(458.912)=(sin(x))/(450) ?

The general solution for (sin(90))/(458.912)=(sin(x))/(450) is x=1.37339…+360n,x=180-1.37339…+360n

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Popular >

(sin(90))/(458.912)=(sin(x))/(450)

Solution

\frac{sin ( 9 0 ^{\circ} )}{458.912} = \frac{sin ( x )}{450}

Solution

x = 1.37339 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.37339 \dots + 36 0^{\circ} n

Radians

x = 1.37339 \dots + 2 πn, x = π - 1.37339 \dots + 2 πn

Solution steps

\frac{sin ( 9 0 ^{\circ} )}{458.912} = \frac{sin ( x )}{450}

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 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}

= 1

= 1

\frac{1}{458.912} = \frac{sin ( x )}{450}

Switch sides

\frac{sin ( x )}{450} = \frac{1}{458.912}

Multiply both sides by

10

\frac{sin ( x )}{450} = \frac{1}{458.912}

Multiply both sides by

10

\frac{sin ( x )}{450} \cdot 10 = \frac{1}{458.912} \cdot 10

Simplify

\frac{sin ( x )}{450} \cdot 10 = \frac{1}{458.912} \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{1}{458.912} \cdot 10 : \frac{10}{458.912}

\frac{1}{458.912} \cdot 10

Multiply fractions:

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

= \frac{1 \cdot 10}{458.912}

Multiply the numbers:

1 \cdot 10 = 10

= \frac{10}{458.912}

\frac{sin ( x )}{45} = \frac{10}{458.912}

\frac{sin ( x )}{45} = \frac{10}{458.912}

\frac{sin ( x )}{45} = \frac{10}{458.912}

Multiply both sides by

45

\frac{sin ( x )}{45} = \frac{10}{458.912}

Multiply both sides by

45

\frac{45 sin ( x )}{45} = \frac{10 \cdot 45}{458.912}

Simplify

\frac{45 sin ( x )}{45} = \frac{10 \cdot 45}{458.912}

Simplify

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

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

Divide the numbers:

\frac{45}{45} = 1

= sin (x)

Simplify

\frac{10 \cdot 45}{458.912} : 0.98058 \dots

\frac{10 \cdot 45}{458.912}

Multiply the numbers:

10 \cdot 45 = 450

= \frac{450}{458.912}

Divide the numbers:

\frac{450}{458.912} = 0.98058 \dots

= 0.98058 \dots

sin (x) = 0.98058 \dots

sin (x) = 0.98058 \dots

sin (x) = 0.98058 \dots

Apply trig inverse properties

sin (x) = 0.98058 \dots

General solutions for

sin (x) = 0.98058 \dots

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

x = arcsin (0.98058 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.98058 \dots) + 36 0^{\circ} n

x = arcsin (0.98058 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.98058 \dots) + 36 0^{\circ} n

Show solutions in decimal form

x = 1.37339 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.37339 \dots + 36 0^{\circ} n

Popular Examples

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0 = \frac{2 π ^{2} cos ( \frac{π x}{10} )}{25}

300cos(70)=375cos(θ)

300 cos (7 0^{\circ}) = 375 cos (θ)

812.25=399.6001+400-1140cos(a)

812.25 = 399.6001 + 400 - 1140 cos (a)

-0.6=sin(2x)

- 0.6 = sin (2 x)

solvefor x,(sin(pix)+cos(piy))^5=36 solve for

x, (sin (π x) + cos (π y))^{5} = 36

Frequently Asked Questions (FAQ)

What is the general solution for (sin(90))/(458.912)=(sin(x))/(450) ?
The general solution for (sin(90))/(458.912)=(sin(x))/(450) is x=1.37339…+360n,x=180-1.37339…+360n