What is the value of sin(2arctan(5/12)) ?

The value of sin(2arctan(5/12)) is 120/169

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2arctan(5/12))

sin (2 arctan (\frac{5}{12}))

\frac{120}{169}

Decimal Notation

0.71005 \dots

Solution steps

sin (2 arctan (\frac{5}{12}))

Rewrite using trig identities:

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

sin (2 arctan (\frac{5}{12}))

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

= 2 sin (arctan (\frac{5}{12})) cos (arctan (\frac{5}{12}))

= 2 sin (arctan (\frac{5}{12})) cos (arctan (\frac{5}{12}))

Rewrite using trig identities:

sin (arctan (\frac{5}{12})) = \frac{5}{13}

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}

Rewrite using trig identities:

cos (arctan (\frac{5}{12})) = \frac{12}{13}

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{12}{13}

= 2 \cdot \frac{5}{13} \cdot \frac{12}{13}

Simplify

2 \cdot \frac{5}{13} \cdot \frac{12}{13} : \frac{120}{169}

2 \cdot \frac{5}{13} \cdot \frac{12}{13}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{5}{13} \cdot \frac{12}{13}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 \cdot 5 \cdot 12}{1 \cdot 13 \cdot 13}

Multiply the numbers:

2 \cdot 5 \cdot 12 = 120

= \frac{120}{1 \cdot 13 \cdot 13}

Multiply the numbers:

1 \cdot 13 \cdot 13 = 169

= \frac{120}{169}

= \frac{120}{169}

tan (\frac{135}{2})

csc (7)

arccos (\frac{4.4}{6.5})

cos (arctan (- 7))

arccos (sin (- \frac{5 π}{3}))

What is the value of sin(2arctan(5/12)) ?
The value of sin(2arctan(5/12)) is 120/169