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

The value of sin(-1/2 pi) is -1

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sin(-1/2 pi)

sin (- \frac{1}{2} π)

- 1

Solution steps

sin (- \frac{1}{2} π)

Simplify:

- \frac{1}{2} π = - \frac{π}{2}

- \frac{1}{2} π

Multiply fractions:

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

= - \frac{1 π}{2}

Multiply:

1 π = π

= - \frac{π}{2}

= sin (- \frac{π}{2})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{2}) = - sin (\frac{π}{2})

= - sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= - 1

cos (57.2957 7^{\circ})

\frac{3}{cos ( 4 5 ^{\circ} )}

6 cos (- \frac{π}{4})

\frac{tan ( 7 3 ^{\circ} ) - tan ( 1 3 ^{\circ} )}{1 + tan ( 7 3 ^{\circ} ) tan ( 1 3 ^{\circ} )}

400 sin (4 5^{\circ})