What is the value of 1/2 cos(2pi) ?

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

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1/2 cos(2pi)

\frac{1}{2} cos (2 π)

\frac{1}{2}

Decimal Notation

0.5

Solution steps

\frac{1}{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

= \frac{1}{2} \cdot 1

Simplify

= \frac{1}{2}

tan (19 π)

\frac{tan ( 4 2 ^{\circ} ) - tan ( 1 2 ^{\circ} )}{1 + tan ( 4 2 ^{\circ} ) tan ( 1 2 ^{\circ} )}

1 + sin (\frac{3 π}{2})

- 2 cos (- π)

5 sin (2 0^{\circ})