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Popular >

cos(pi/8*16)

Solution

cos (\frac{π}{8} \cdot 16)

Solution

1

Solution steps

cos (\frac{π}{8} \cdot 16)

Simplify:

\frac{π}{8} \cdot 16 = 2 π

\frac{π}{8} \cdot 16

Multiply fractions:

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

= \frac{π 16}{8}

Divide the numbers:

\frac{16}{8} = 2

= 2 π

= cos (2 π)

cos (2 π) = cos (0)

cos (2 π)

Rewrite

2 π

as

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

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Frequently Asked Questions (FAQ)

What is the value of cos(pi/8*16) ?
The value of cos(pi/8*16) is 1