What is the value of sin(arctan(5/12)) ?

The value of sin(arctan(5/12)) is 5/13

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(arctan(5/12))

sin (arctan (\frac{5}{12}))

\frac{5}{13}

Decimal Notation

0.38461 \dots

Solution steps

sin (arctan (\frac{5}{12}))

Rewrite using trig identities:

sin (arctan (\frac{5}{12})) = \frac{( \frac{5}{12} ) 1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{5}{12} ) 1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

= \frac{\frac{5}{12} 1 + ( \frac{5}{12} ) ^{2}}{1 + ( \frac{5}{12} ) ^{2}}

Simplify

= \frac{5}{13}

- 3 cos (0)

arctan (- \frac{12}{5})

2 cos (2 0^{\circ})

cot (7 5^{\circ})

cos (- 19 5^{\circ})