What is the general solution for -cos(x)= 2/(sqrt(20)) ?

The general solution for -cos(x)= 2/(sqrt(20)) is x=2.03444…+2pin,x=-2.03444…+2pin

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Popular >

-cos(x)= 2/(sqrt(20))

Solution

- cos (x) = \frac{2}{20}

Solution

x = 2.03444 \dots + 2 πn, x = - 2.03444 \dots + 2 πn

Degrees

x = 116.56505 \dots^{\circ} + 36 0^{\circ} n, x = - 116.56505 \dots^{\circ} + 36 0^{\circ} n

Solution steps

- cos (x) = \frac{2}{20}

20 = 25

20

Prime factorization of

20 : 2^{2} \cdot 5

20

20

divides by

220 = 10 \cdot 2

= 2 \cdot 10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5

= 2^{2} \cdot 5

= 2^{2} \cdot 5

Apply radical rule:

= 5 2^{2}

Apply radical rule:

2^{2} = 2

= 25

- cos (x) = \frac{2}{2 5}

Divide the numbers:

\frac{2}{2} = 1

- cos (x) = \frac{1}{5}

Divide both sides by

- 1

- cos (x) = \frac{1}{5}

Divide both sides by

- 1

\frac{- cos ( x )}{- 1} = \frac{\frac{1}{5}}{- 1}

Simplify

\frac{- cos ( x )}{- 1} = \frac{\frac{1}{5}}{- 1}

Simplify

\frac{- cos ( x )}{- 1} : cos (x)

\frac{- cos ( x )}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{cos ( x )}{1}

Apply rule

\frac{a}{1} = a

= cos (x)

Simplify

\frac{\frac{1}{5}}{- 1} : - \frac{5}{5}

\frac{\frac{1}{5}}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{1}{5}}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{\frac{1}{5}}{1} = \frac{1}{5}

= - \frac{1}{5}

Rationalize

- \frac{1}{5} : - \frac{5}{5}

- \frac{1}{5}

Multiply by the conjugate

\frac{5}{5}

= - \frac{1 \cdot 5}{5 5}

1 \cdot 5 = 5

55 = 5

55

Apply radical rule:

a a = a

55 = 5

= 5

= - \frac{5}{5}

= - \frac{5}{5}

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

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

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

Apply trig inverse properties

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

General solutions for

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

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

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

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

Show solutions in decimal form

x = 2.03444 \dots + 2 πn, x = - 2.03444 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for -cos(x)= 2/(sqrt(20)) ?
The general solution for -cos(x)= 2/(sqrt(20)) is x=2.03444…+2pin,x=-2.03444…+2pin