What is the value of arcsin^2((sqrt(2))/2) ?

The value of arcsin^2((sqrt(2))/2) is (pi^2)/(16)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

arcsin^2((sqrt(2))/2)

arcsin^{2} (\frac{2}{2})

\frac{π ^{2}}{16}

Decimal

35.34

Solution steps

arcsin^{2} (\frac{2}{2})

Use the following trivial identity:

arcsin (\frac{2}{2}) = \frac{π}{4}

arcsin (\frac{2}{2})

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{4}

= (\frac{π}{4})^{2}

Simplify

(\frac{π}{4})^{2} : \frac{π ^{2}}{16}

(\frac{π}{4})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{π ^{2}}{4 ^{2}}

4^{2} = 16

= \frac{π ^{2}}{16}

= \frac{π ^{2}}{16}

What is the value of arcsin^2((sqrt(2))/2) ?
The value of arcsin^2((sqrt(2))/2) is (pi^2)/(16)