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

The value of cos(pi/2+2pi) is 0

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cos(pi/2+2pi)

cos (\frac{π}{2} + 2 π)

0

Solution steps

cos (\frac{π}{2} + 2 π)

Simplify:

\frac{π}{2} + 2 π = \frac{5 π}{2}

\frac{π}{2} + 2 π

Convert element to fraction:

2 π = \frac{2 π 2}{2}

= \frac{π}{2} + \frac{2 π 2}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{π + 2 π 2}{2}

π + 2 π 2 = 5 π

π + 2 π 2

Multiply the numbers:

2 \cdot 2 = 4

= π + 4 π

Add similar elements:

π + 4 π = 5 π

= 5 π

= \frac{5 π}{2}

= cos (\frac{5 π}{2})

cos (\frac{5 π}{2}) = cos (\frac{π}{2})

cos (\frac{5 π}{2})

Rewrite

\frac{5 π}{2}

2 π + \frac{π}{2}

= cos (2 π + \frac{π}{2})

Apply the periodicity of

cos

cos (x + 2 π) = cos (x)

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

= cos (\frac{π}{2})

= cos (\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

= 0

arctan (\frac{1}{14})

3 tan (\frac{5 π}{6})

20 sin (3 2^{\circ})

tan^{2} (6 0^{\circ}) sec (3 0^{\circ}) sin (4 5^{\circ})

\frac{14.088}{tan ( 117.1 3 ^{\circ} )}