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

The value of sin(2(-pi/2)) is 0

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sin(2(-pi/2))

sin (2 (- \frac{π}{2}))

0

Solution steps

sin (2 (- \frac{π}{2}))

Simplify:

2 (- \frac{π}{2}) = - π

2 (- \frac{π}{2})

Remove parentheses:

(- a) = - a

= - 2 \cdot \frac{π}{2}

Multiply fractions:

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

= - \frac{π 2}{2}

Cancel the common factor:

2

= - π

= sin (- π)

Use the following property:

sin (- x) = - sin (x)

sin (- π) = - sin (π)

= - sin (π)

Use the following trivial identity:

sin (π) = 0

sin (π)

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}

= 0

= - 0

Simplify

= 0

cos (\frac{π}{3})

(0) - arctan (0)

3 \cdot tan (6 0^{\circ})

arctan (\frac{7}{- 10})

25 cos (5 0^{\circ})