What is the general solution for cos(x)=-(22)/(7.28*sqrt(20)) ?

The general solution for cos(x)=-(22)/(7.28*sqrt(20)) is x=2.31275…+2pin,x=-2.31275…+2pin

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cos(x)=-(22)/(7.28*sqrt(20))

cos (x) = - \frac{22}{7.28 \cdot 20}

x = 2.31275 \dots + 2 πn, x = - 2.31275 \dots + 2 πn

Radians

x = 2.31275 \dots + 6.28318 \dots n, x = - 2.31275 \dots + 6.28318 \dots n

Solution steps

cos (x) = - \frac{22}{7.28 20}

Simplify

- \frac{22}{7.28 20} : - \frac{11 5}{36.4}

- \frac{22}{7.28 20}

Cancel

\frac{22}{7.28 20} : \frac{11}{5 \cdot 7.28}

\frac{22}{7.28 20}

Factor

22 : 2 \cdot 11

Factor

22 = 2 \cdot 11

Factor

20 : 25

Factor

20 = 2^{2} \cdot 5

= 2^{2} \cdot 5

Apply radical rule:

= 5 2^{2}

Simplify

2^{2} : 2

2^{2}

Apply radical rule:

assuming

a \geq 0

= 2

= 25

= \frac{2 \cdot 11}{2 5 \cdot 7.28}

Divide the numbers:

\frac{2}{2} = 1

= \frac{11}{5 \cdot 7.28}

= - \frac{11}{5 \cdot 7.28}

Rationalize

- \frac{11}{5 \cdot 7.28} : - \frac{11 5}{36.4}

- \frac{11}{5 \cdot 7.28}

Multiply by the conjugate

\frac{5}{5}

= - \frac{11 5}{5 \cdot 7.28 5}

5 \cdot 7.28 5 = 36.4

5 \cdot 7.28 5

Apply radical rule:

a a = a

55 = 5

= 5 \cdot 7.28

Multiply the numbers:

7.28 \cdot 5 = 36.4

= 36.4

= - \frac{11 5}{36.4}

= - \frac{11 5}{36.4}

cos (x) = - \frac{11 5}{36.4}

Apply trig inverse properties

cos (x) = - \frac{11 5}{36.4}

General solutions for

cos (x) = - \frac{11 5}{36.4}

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

x = arccos (- \frac{11 5}{36.4}) + 2 πn, x = - arccos (- \frac{11 5}{36.4}) + 2 πn

x = arccos (- \frac{11 5}{36.4}) + 2 πn, x = - arccos (- \frac{11 5}{36.4}) + 2 πn

Show solutions in decimal form

x = 2.31275 \dots + 2 πn, x = - 2.31275 \dots + 2 πn

What is the general solution for cos(x)=-(22)/(7.28*sqrt(20)) ?
The general solution for cos(x)=-(22)/(7.28*sqrt(20)) is x=2.31275…+2pin,x=-2.31275…+2pin