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

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

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cos(pi/2)-pi/2 sin(pi/2)

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

- \frac{π}{2}

Decimal Notation

- 1.57079 \dots

Solution steps

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

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

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

= 0 - \frac{π}{2} \cdot 1

Simplify

= - \frac{π}{2}

1000 cos (3 0^{\circ})

cot (\frac{π}{9})

2 cos (\frac{π}{2}) + sin (2 (\frac{π}{2}))

300 \cdot cos (5 5^{\circ}) \cdot 42

20 cos (5 5^{\circ})

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