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Popular Trigonometry >

cos(2.5pi)

Solution

cos (2.5 π)

Solution

0

Solution steps

cos (2.5 π)

= cos (\frac{5}{2} π)

Simplify:

\frac{5}{2} π = \frac{5 π}{2}

\frac{5}{2} π

Multiply fractions:

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

= \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}

as

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

Popular Examples

12.4-10(0.5pi-arcsin(0.5)-0.5(1-(0.5)^2)^{1/2})

(1.24)/(tan(34))

(sin(30))/(sin(22))

Frequently Asked Questions (FAQ)

What is the value of cos(2.5pi) ?
The value of cos(2.5pi) is 0