What is the value of arccos(8/(sqrt(26))) ?

The value of arccos(8/(sqrt(26))) is No Solution for x\in\mathbb{R}

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arccos(8/(sqrt(26)))

arccos (\frac{8}{26})

No Solution for x \in R

Solution steps

arccos (\frac{8}{26})

Simplify:

\frac{8}{26} = \frac{4 26}{13}

\frac{8}{26}

Factor

8 : 2^{3}

Factor

8 = 2^{3}

Factor

26 : 213

Factor

26 = 2 \cdot 13

= 2 \cdot 13

Apply radical rule:

= 213

= \frac{2 ^{3}}{2 13}

Cancel

\frac{2 ^{3}}{2 13} : \frac{2 ^{\frac{5}{2}}}{13}

\frac{2 ^{3}}{2 13}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{2 ^{3}}{2 ^{\frac{1}{2}} 13}

Apply exponent rule:

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

\frac{2 ^{3}}{2 ^{\frac{1}{2}}} = 2^{3 - \frac{1}{2}}

= \frac{2 ^{3 - \frac{1}{2}}}{13}

Subtract the numbers:

3 - \frac{1}{2} = \frac{5}{2}

= \frac{2 ^{\frac{5}{2}}}{13}

= \frac{2 ^{\frac{5}{2}}}{13}

2^{\frac{5}{2}} = 2^{2} 2

2^{\frac{5}{2}}

2^{\frac{5}{2}} = 2^{2 + \frac{1}{2}}

= 2^{2 + \frac{1}{2}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

= 2^{2} \cdot 2^{\frac{1}{2}}

Refine

= 2^{2} 2

= \frac{2 ^{2} 2}{13}

2^{2} = 4

= \frac{4 2}{13}

Rationalize

\frac{4 2}{13} : \frac{4 26}{13}

\frac{4 2}{13}

Multiply by the conjugate

\frac{13}{13}

= \frac{4 2 13}{13 13}

4213 = 426

4213

Apply radical rule:

a b = a \cdot b

213 = 2 \cdot 13

= 4 2 \cdot 13

Multiply the numbers:

2 \cdot 13 = 26

= 426

1313 = 13

1313

Apply radical rule:

a a = a

1313 = 13

= 13

= \frac{4 26}{13}

= \frac{4 26}{13}

= arccos (\frac{4 26}{13})

Real domain for

arccos (x)

- 1 \leq x \leq 1

No Solution for x \in R

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What is the value of arccos(8/(sqrt(26))) ?
The value of arccos(8/(sqrt(26))) is No Solution for x\in\mathbb{R}