What is the general solution for 14928=(18177)/((1+0.387cos(x))) ?

The general solution for 14928=(18177)/((1+0.387cos(x))) is x=0.97352…+2pin,x=2pi-0.97352…+2pin

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14928=(18177)/((1+0.387cos(x)))

Solution

14928 = \frac{18177}{( 1 + 0.387 cos ( x ) )}

Solution

x = 0.97352 \dots + 2 πn, x = 2 π - 0.97352 \dots + 2 πn

Degrees

x = 55.77879 \dots^{\circ} + 36 0^{\circ} n, x = 304.22120 \dots^{\circ} + 36 0^{\circ} n

Solution steps

14928 = \frac{18177}{( 1 + 0.387 cos ( x ) )}

Switch sides

\frac{18177}{1 + 0.387 cos ( x )} = 14928

Multiply both sides by

1 + 0.387 cos (x)

\frac{18177}{1 + 0.387 cos ( x )} = 14928

Multiply both sides by

1 + 0.387 cos (x)

\frac{18177}{1 + 0.387 cos ( x )} (1 + 0.387 cos (x)) = 14928 (1 + 0.387 cos (x))

Simplify

18177 = 14928 (1 + 0.387 cos (x))

18177 = 14928 (1 + 0.387 cos (x))

Switch sides

14928 (1 + 0.387 cos (x)) = 18177

Divide both sides by

14928

14928 (1 + 0.387 cos (x)) = 18177

Divide both sides by

14928

\frac{14928 ( 1 + 0.387 cos ( x ) )}{14928} = \frac{18177}{14928}

Simplify

1 + 0.387 cos (x) = \frac{6059}{4976}

1 + 0.387 cos (x) = \frac{6059}{4976}

Move

1

to the right side

1 + 0.387 cos (x) = \frac{6059}{4976}

Subtract

1

from both sides

1 + 0.387 cos (x) - 1 = \frac{6059}{4976} - 1

Simplify

1 + 0.387 cos (x) - 1 = \frac{6059}{4976} - 1

Simplify

1 + 0.387 cos (x) - 1 : 0.387 cos (x)

1 + 0.387 cos (x) - 1

Add similar elements:

1 - 1 = 0

= 0.387 cos (x)

Simplify

\frac{6059}{4976} - 1 : \frac{1083}{4976}

\frac{6059}{4976} - 1

Convert element to fraction:

1 = \frac{1 \cdot 4976}{4976}

= - \frac{1 \cdot 4976}{4976} + \frac{6059}{4976}

Since the denominators are equal, combine the fractions:

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

= \frac{- 1 \cdot 4976 + 6059}{4976}

- 1 \cdot 4976 + 6059 = 1083

- 1 \cdot 4976 + 6059

Multiply the numbers:

1 \cdot 4976 = 4976

= - 4976 + 6059

Add/Subtract the numbers:

- 4976 + 6059 = 1083

= 1083

= \frac{1083}{4976}

0.387 cos (x) = \frac{1083}{4976}

0.387 cos (x) = \frac{1083}{4976}

0.387 cos (x) = \frac{1083}{4976}

Divide both sides by

0.387

0.387 cos (x) = \frac{1083}{4976}

Divide both sides by

0.387

\frac{0.387 cos ( x )}{0.387} = \frac{\frac{1083}{4976}}{0.387}

Simplify

\frac{0.387 cos ( x )}{0.387} = \frac{\frac{1083}{4976}}{0.387}

Simplify

\frac{0.387 cos ( x )}{0.387} : cos (x)

\frac{0.387 cos ( x )}{0.387}

Cancel the common factor:

0.387

= cos (x)

Simplify

\frac{\frac{1083}{4976}}{0.387} : 0.56238 \dots

\frac{\frac{1083}{4976}}{0.387}

Apply the fraction rule:

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

= \frac{1083}{4976 \cdot 0.387}

Multiply the numbers:

4976 \cdot 0.387 = 1925.712

= \frac{1083}{1925.712}

Divide the numbers:

\frac{1083}{1925.712} = 0.56238 \dots

= 0.56238 \dots

cos (x) = 0.56238 \dots

cos (x) = 0.56238 \dots

cos (x) = 0.56238 \dots

Verify Solutions

Find undefined (singularity) points:

cos (x) = - \frac{1000}{387}

Take the denominator(s) of

\frac{18177}{1 + 0.387 cos ( x )}

and compare to zero

Solve

1 + 0.387 cos (x) = 0 : cos (x) = - \frac{1000}{387}

1 + 0.387 cos (x) = 0

Multiply both sides by

1000

1 + 0.387 cos (x) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

1 \cdot 1000 + 0.387 cos (x) \cdot 1000 = 0 \cdot 1000

Refine

1000 + 387 cos (x) = 0

1000 + 387 cos (x) = 0

Move

1000

to the right side

1000 + 387 cos (x) = 0

Subtract

1000

from both sides

1000 + 387 cos (x) - 1000 = 0 - 1000

Simplify

387 cos (x) = - 1000

387 cos (x) = - 1000

Divide both sides by

387

387 cos (x) = - 1000

Divide both sides by

387

\frac{387 cos ( x )}{387} = \frac{- 1000}{387}

Simplify

cos (x) = - \frac{1000}{387}

cos (x) = - \frac{1000}{387}

The following points are undefined

cos (x) = - \frac{1000}{387}

Combine undefined points with solutions:

cos (x) = 0.56238 \dots

Apply trig inverse properties

cos (x) = 0.56238 \dots

General solutions for

cos (x) = 0.56238 \dots

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

x = arccos (0.56238 \dots) + 2 πn, x = 2 π - arccos (0.56238 \dots) + 2 πn

x = arccos (0.56238 \dots) + 2 πn, x = 2 π - arccos (0.56238 \dots) + 2 πn

Show solutions in decimal form

x = 0.97352 \dots + 2 πn, x = 2 π - 0.97352 \dots + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 14928=(18177)/((1+0.387cos(x))) ?
The general solution for 14928=(18177)/((1+0.387cos(x))) is x=0.97352…+2pin,x=2pi-0.97352…+2pin