What is the value of tan(arcsin(8/9)) ?

The value of tan(arcsin(8/9)) is (8sqrt(17))/(17)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(arcsin(8/9))

tan (arcsin (\frac{8}{9}))

\frac{8 17}{17}

Decimal Notation

1.94028 \dots

Solution steps

tan (arcsin (\frac{8}{9}))

Rewrite using trig identities:

tan (arcsin (\frac{8}{9})) = \frac{( \frac{8}{9} ) 1 - ( \frac{8}{9} ) ^{2}}{1 - ( \frac{8}{9} ) ^{2}}

Use the following identity:

tan (arcsin (x)) = \frac{x 1 - x ^{2}}{1 - x ^{2}}

= \frac{( \frac{8}{9} ) 1 - ( \frac{8}{9} ) ^{2}}{1 - ( \frac{8}{9} ) ^{2}}

= \frac{\frac{8}{9} 1 - ( \frac{8}{9} ) ^{2}}{1 - ( \frac{8}{9} ) ^{2}}

Simplify

= \frac{8 17}{17}

arcsin (sin (\frac{11 π}{4}))

arccos (\frac{2}{3})

- csc^{2} (\frac{5 π}{6})

cos (63 0^{\circ})

arccos (\frac{5}{4})

What is the value of tan(arcsin(8/9)) ?
The value of tan(arcsin(8/9)) is (8sqrt(17))/(17)