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

The value of sqrt(2)cos(2pi) is square root of 2

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sqrt(2)cos(2pi)

2 cos (2 π)

2

Decimal Notation

1.41421 \dots

Solution steps

2 cos (2 π)

Rewrite using trig identities:

cos (2 π) = 1

cos (2 π)

cos (2 π) = cos (0)

cos (2 π)

Rewrite

2 π

2 π + 0

= cos (2 π + 0)

Apply the periodicity of

cos

cos (x + 2 π) = cos (x)

cos (2 π + 0) = cos (0)

= cos (0)

= cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

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

= 2 \cdot 1

Simplify

= 2

\frac{0.5}{sin ( 0.5 )}

18 sin (7 3^{\circ})

(- 3 + i) (\frac{1}{8} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})))

arccos (\frac{2}{4})

sin (\frac{25 π}{3})

What is the value of sqrt(2)cos(2pi) ?
The value of sqrt(2)cos(2pi) is square root of 2