What is the value of tan(arcsin(5/13)+pi/6) ?

The value of tan(arcsin(5/13)+pi/6) is (240+169sqrt(3))/(407)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(arcsin(5/13)+pi/6)

tan (arcsin (\frac{5}{13}) + \frac{π}{6})

\frac{240 + 169 3}{407}

Solution steps

tan (arcsin (\frac{5}{13}) + \frac{π}{6})

Rewrite using trig identities:

\frac{tan ( arcsin ( \frac{5}{13} ) ) + tan ( \frac{π}{6} )}{1 - tan ( arcsin ( \frac{5}{13} ) ) tan ( \frac{π}{6} )}

= \frac{tan ( arcsin ( \frac{5}{13} ) ) + tan ( \frac{π}{6} )}{1 - tan ( arcsin ( \frac{5}{13} ) ) tan ( \frac{π}{6} )}

Rewrite using trig identities:

tan (arcsin (\frac{5}{13})) = \frac{5}{12}

Use the following trivial identity:

tan (\frac{π}{6}) = \frac{3}{3}

= \frac{\frac{5}{12} + \frac{3}{3}}{1 - \frac{5}{12} \cdot \frac{3}{3}}

Simplify

\frac{\frac{5}{12} + \frac{3}{3}}{1 - \frac{5}{12} \cdot \frac{3}{3}} : \frac{240 + 169 3}{407}

= \frac{240 + 169 3}{407}

cos (2 arccos (- \frac{2}{2}))

arccos (\frac{1}{11})

arctan (2 + 3)

sin (9 0^{\circ} + 3 0^{\circ})

cos (arctan (\frac{1}{2}) - 3 π)

What is the value of tan(arcsin(5/13)+pi/6) ?
The value of tan(arcsin(5/13)+pi/6) is (240+169sqrt(3))/(407)