What is the value of picos(pi*1) ?

The value of picos(pi*1) is -pi

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picos(pi*1)

π cos (π \cdot 1)

- π

Decimal Notation

- 3.14159 \dots

Solution steps

π cos (π 1)

Rewrite using trig identities:

cos (π 1) = - 1

cos (π 1)

Simplify

= 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

= π (- 1)

Simplify

= - π

arccos (cos (- π))

sin (4 \frac{4 π}{3})

sin (14 8^{\circ})

cos (\frac{2 π}{3} + \frac{π}{4})

cos^{2} (6 0^{\circ}) - cos^{2} (3 0^{\circ})