What is the value of tan(arcsin(2/3)) ?

The value of tan(arcsin(2/3)) is (2sqrt(5))/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(arcsin(2/3))

tan (arcsin (\frac{2}{3}))

\frac{2 5}{5}

Decimal Notation

0.89442 \dots

Solution steps

tan (arcsin (\frac{2}{3}))

Rewrite using trig identities:

tan (arcsin (\frac{2}{3})) = \frac{( \frac{2}{3} ) 1 - ( \frac{2}{3} ) ^{2}}{1 - ( \frac{2}{3} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{2}{3} ) 1 - ( \frac{2}{3} ) ^{2}}{1 - ( \frac{2}{3} ) ^{2}}

= \frac{\frac{2}{3} 1 - ( \frac{2}{3} ) ^{2}}{1 - ( \frac{2}{3} ) ^{2}}

Simplify

= \frac{2 5}{5}

3 cos (\frac{π}{3})

cot (\frac{8 π}{3})

cos (68 6^{\circ}) sec (3 4^{\circ}) + cos (1 8^{\circ}) sin (- 7 2^{\circ})

sec (arctan (2))

arccos (\frac{2}{5})

What is the value of tan(arcsin(2/3)) ?
The value of tan(arcsin(2/3)) is (2sqrt(5))/5