What is the value of arcsin(0.5)-e^{-2(0.5)} ?

The value of arcsin(0.5)-e^{-2(0.5)} is pi/6-1/e

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arcsin(0.5)-e^{-2(0.5)}

arcsin (0.5) - e^{- 2 (0.5)}

\frac{π}{6} - \frac{1}{e}

Decimal

8.92

Solution steps

arcsin (0.5) - e^{- 2 (0.5)}

= arcsin (\frac{1}{2}) - e^{- 2 \cdot \frac{1}{2}}

Use the following trivial identity:

arcsin (\frac{1}{2}) = \frac{π}{6}

arcsin (\frac{1}{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}{6}

= \frac{π}{6} - e^{- 2 \cdot \frac{1}{2}}

Simplify

\frac{π}{6} - e^{- 2 \cdot \frac{1}{2}} : \frac{π}{6} - \frac{1}{e}

\frac{π}{6} - e^{- 2 \cdot \frac{1}{2}}

Multiply

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

2

= - 1

= \frac{π}{6} - e^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \frac{π}{6} - \frac{1}{e}

= \frac{π}{6} - \frac{1}{e}

What is the value of arcsin(0.5)-e^{-2(0.5)} ?
The value of arcsin(0.5)-e^{-2(0.5)} is pi/6-1/e