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

The value of 2arcsin(-1/2) is -pi/3

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2arcsin(-1/2)

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

- \frac{π}{3}

Decimal Notation

- 60

Solution steps

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

Rewrite using trig identities:

arcsin (- \frac{1}{2}) = - \frac{π}{6}

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

Use the following property:

arcsin (- x) = - arcsin (x)

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

= - arcsin (\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}

= 2 (- \frac{π}{6})

Simplify

2 (- \frac{π}{6}) : - \frac{π}{3}

2 (- \frac{π}{6})

Remove parentheses:

(- a) = - a

= - 2 \cdot \frac{π}{6}

Multiply fractions:

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

= - \frac{π 2}{6}

Cancel the common factor:

2

= - \frac{π}{3}

= - \frac{π}{3}

2 - cos (\frac{π}{2})

sec (- \frac{13 π}{4})

arccos (\frac{4}{4 2})

- 2 sec (9 0^{\circ})

arctan (1.44)