What is the value of sin(arctan(7/24)) ?

The value of sin(arctan(7/24)) is 7/25

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(arctan(7/24))

sin (arctan (\frac{7}{24}))

\frac{7}{25}

Decimal Notation

0.28

Solution steps

sin (arctan (\frac{7}{24}))

Rewrite using trig identities:

sin (arctan (\frac{7}{24})) = \frac{( \frac{7}{24} ) 1 + ( \frac{7}{24} ) ^{2}}{1 + ( \frac{7}{24} ) ^{2}}

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{( \frac{7}{24} ) 1 + ( \frac{7}{24} ) ^{2}}{1 + ( \frac{7}{24} ) ^{2}}

= \frac{\frac{7}{24} 1 + ( \frac{7}{24} ) ^{2}}{1 + ( \frac{7}{24} ) ^{2}}

Simplify

= \frac{7}{25}

\frac{500}{sin ( 1 0 ^{\circ} )}

sin (3 5^{\circ}) \cdot 78

arctan (0.28)

arctan (0.15)

arctan (0.46)