What is the general solution for 4674.04= 5/(3cos(x))*2804.42 ?

The general solution for 4674.04= 5/(3cos(x))*2804.42 is x=0.00168…+2pin,x=2pi-0.00168…+2pin

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Popular Trigonometry >

4674.04= 5/(3cos(x))*2804.42

Solution

4674.04 = \frac{5}{3 cos ( x )} \cdot 2804.42

Solution

x = 0.00168 \dots + 2 πn, x = 2 π - 0.00168 \dots + 2 πn

Degrees

x = 0.09677 \dots^{\circ} + 36 0^{\circ} n, x = 359.90322 \dots^{\circ} + 36 0^{\circ} n

Solution steps

4674.04 = \frac{5}{3 cos ( x )} \cdot 2804.42

Switch sides

\frac{5}{3 cos ( x )} \cdot 2804.42 = 4674.04

Multiply both sides by

100

\frac{5}{3 cos ( x )} \cdot 2804.42 = 4674.04

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

2

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

100

\frac{5}{3 cos ( x )} \cdot 2804.42 \cdot 100 = 4674.04 \cdot 100

Refine

\frac{1402210}{3 cos ( x )} = 467404

\frac{1402210}{3 cos ( x )} = 467404

Multiply both sides by

cos (x)

\frac{1402210}{3 cos ( x )} = 467404

Multiply both sides by

cos (x)

\frac{1402210}{3 cos ( x )} cos (x) = 467404 cos (x)

Simplify

\frac{1402210}{3} = 467404 cos (x)

\frac{1402210}{3} = 467404 cos (x)

Switch sides

467404 cos (x) = \frac{1402210}{3}

Divide both sides by

467404

467404 cos (x) = \frac{1402210}{3}

Divide both sides by

467404

\frac{467404 cos ( x )}{467404} = \frac{\frac{1402210}{3}}{467404}

Simplify

\frac{467404 cos ( x )}{467404} = \frac{\frac{1402210}{3}}{467404}

Simplify

\frac{467404 cos ( x )}{467404} : cos (x)

\frac{467404 cos ( x )}{467404}

Divide the numbers:

\frac{467404}{467404} = 1

= cos (x)

Simplify

\frac{\frac{1402210}{3}}{467404} : \frac{701105}{701106}

\frac{\frac{1402210}{3}}{467404}

Apply the fraction rule:

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

= \frac{1402210}{3 \cdot 467404}

Multiply the numbers:

3 \cdot 467404 = 1402212

= \frac{1402210}{1402212}

Cancel the common factor:

2

= \frac{701105}{701106}

cos (x) = \frac{701105}{701106}

cos (x) = \frac{701105}{701106}

cos (x) = \frac{701105}{701106}

Verify Solutions

Find undefined (singularity) points:

cos (x) = 0

Take the denominator(s) of

\frac{5}{3 cos ( x )} 2804.42

and compare to zero

Solve

3 cos (x) = 0 : cos (x) = 0

3 cos (x) = 0

Divide both sides by

3

3 cos (x) = 0

Divide both sides by

3

\frac{3 cos ( x )}{3} = \frac{0}{3}

Simplify

cos (x) = 0

cos (x) = 0

The following points are undefined

cos (x) = 0

Combine undefined points with solutions:

cos (x) = \frac{701105}{701106}

Apply trig inverse properties

cos (x) = \frac{701105}{701106}

General solutions for

cos (x) = \frac{701105}{701106}

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

x = arccos (\frac{701105}{701106}) + 2 πn, x = 2 π - arccos (\frac{701105}{701106}) + 2 πn

x = arccos (\frac{701105}{701106}) + 2 πn, x = 2 π - arccos (\frac{701105}{701106}) + 2 πn

Show solutions in decimal form

x = 0.00168 \dots + 2 πn, x = 2 π - 0.00168 \dots + 2 πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 4674.04= 5/(3cos(x))*2804.42 ?
The general solution for 4674.04= 5/(3cos(x))*2804.42 is x=0.00168…+2pin,x=2pi-0.00168…+2pin