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

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

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cos(pi/2 (2))

cos (\frac{π}{2} (2))

- 1

Solution steps

cos (\frac{π}{2} (2))

= cos (\frac{π}{2} \cdot 2)

Simplify:

\frac{π}{2} \cdot 2 = π

\frac{π}{2} \cdot 2

Multiply fractions:

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

= \frac{π 2}{2}

Cancel the common factor:

2

= π

= cos (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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}

= (- 1)

= - 1

0.6 \cdot sin (3 0^{\circ})

sin (- 2 \frac{π}{6}) + cos (\frac{π}{6})

cos (0.8027)

arccos (\frac{7}{53})

5 sin (1)