What is the value of arcsin((-1)/(sqrt(2))) ?

The value of arcsin((-1)/(sqrt(2))) is -pi/4

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arcsin((-1)/(sqrt(2)))

arcsin (\frac{- 1}{2})

- \frac{π}{4}

Decimal Notation

- 45

Solution steps

arcsin (\frac{- 1}{2})

Simplify:

\frac{- 1}{2} = - \frac{2}{2}

\frac{- 1}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{2}

Rationalize

- \frac{1}{2} : - \frac{2}{2}

- \frac{1}{2}

Multiply by the conjugate

\frac{2}{2}

= - \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= - \frac{2}{2}

= - \frac{2}{2}

= arcsin (- \frac{2}{2})

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{2}) = - arcsin (\frac{2}{2})

= - arcsin (\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}

3 π + sin^{2} (\frac{3 π}{3}) - 8

arccos (0.87)

arccos (0.28)

sin^{2} (2 0^{\circ}) + cos^{2} (2 0^{\circ})

cos (- 6)

What is the value of arcsin((-1)/(sqrt(2))) ?
The value of arcsin((-1)/(sqrt(2))) is -pi/4