What is the value of sin((arcsin(4))/5+(arctan(3))/4) ?

The value of sin((arcsin(4))/5+(arctan(3))/4) is No Solution for x\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

sin((arcsin(4))/5+(arctan(3))/4)

sin (\frac{arcsin ( 4 )}{5} + \frac{arctan ( 3 )}{4})

No Solution for x \in R

Solution steps

sin (\frac{arcsin ( 4 )}{5} + \frac{arctan ( 3 )}{4})

Simplify:

\frac{arcsin ( 4 )}{5} + \frac{arctan ( 3 )}{4} = \frac{4 arcsin ( 4 ) + 5 arctan ( 3 )}{20}

\frac{arcsin ( 4 )}{5} + \frac{arctan ( 3 )}{4}

Least Common Multiplier of

5, 4 : 20

5, 4

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Multiply each factor the greatest number of times it occurs in either

5

4

= 5 \cdot 2 \cdot 2

Multiply the numbers:

5 \cdot 2 \cdot 2 = 20

= 20

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

20

For

\frac{arcsin ( 4 )}{5} :

multiply the denominator and numerator by

4

\frac{arcsin ( 4 )}{5} = \frac{arcsin ( 4 ) \cdot 4}{5 \cdot 4} = \frac{arcsin ( 4 ) \cdot 4}{20}

For

\frac{arctan ( 3 )}{4} :

multiply the denominator and numerator by

5

\frac{arctan ( 3 )}{4} = \frac{arctan ( 3 ) \cdot 5}{4 \cdot 5} = \frac{arctan ( 3 ) \cdot 5}{20}

= \frac{arcsin ( 4 ) \cdot 4}{20} + \frac{arctan ( 3 ) \cdot 5}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{arcsin ( 4 ) \cdot 4 + arctan ( 3 ) \cdot 5}{20}

= sin (\frac{4 arcsin ( 4 ) + 5 arctan ( 3 )}{20})

Real domain for

arcsin (x)

- 1 \leq x \leq 1

No Solution for x \in R

What is the value of sin((arcsin(4))/5+(arctan(3))/4) ?
The value of sin((arcsin(4))/5+(arctan(3))/4) is No Solution for x\in\mathbb{R}