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

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

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

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

\frac{π}{2}

Decimal Notation

90

Solution steps

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

Use the following trivial identity:

arcsin (\frac{1}{2}) = \frac{π}{4}

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}{4}

= 2 \cdot \frac{π}{4}

Simplify

2 \cdot \frac{π}{4} : \frac{π}{2}

2 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 2}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2}

tan (arccos (0.95)) - tan (arccos (0.8))

2 sin (3 8^{\circ}) cos (3 8^{\circ})

600 - \frac{220}{sin ( 3 7 ^{\circ} )} sin (3 7^{\circ})

tan (\frac{10}{6})

cos^{4} (21. 2^{\circ}) + 0.01013 - 0.8809 cos^{2} (21. 2^{\circ})

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