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

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

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1/2 sin(-pi/2)

\frac{1}{2} sin (- \frac{π}{2})

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

\frac{1}{2} sin (- \frac{π}{2})

Rewrite using trig identities:

sin (- \frac{π}{2}) = - 1

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

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

Simplify

= - \frac{1}{2}

3 (cos (12 0^{\circ}) + i sin (12 0^{\circ}))

sin (4 \frac{π}{3})

sin (4 \frac{π}{4})

sin (103 5^{\circ})

sin^{4} (9 0^{\circ})