What is the value of 0.15cos(2pi*0.25) ?

The value of 0.15cos(2pi*0.25) is 0

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0.15cos(2pi*0.25)

0.15 cos (2 π \cdot 0.25)

0

Solution steps

0.15 cos (2 π 0.25)

= \frac{3}{20} cos (2 π \frac{1}{4})

Rewrite using trig identities:

cos (2 π \frac{1}{4}) = 0

cos (2 π \frac{1}{4})

Simplify:

2 π \frac{1}{4} = \frac{π}{2}

2 π \frac{1}{4}

Multiply fractions:

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

= \frac{1 \cdot 2 π}{4}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2 π}{4}

Cancel the common factor:

2

= \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

= \frac{3}{20} \cdot 0

Simplify

= 0

24 sin (4 5^{\circ})

10 \cdot 6 \cdot cos (12 0^{\circ})

cos (2 arctan (\frac{9}{40}))

\frac{5}{cos ( 4 2 ^{\circ} )}

\frac{sin ^{2} ( 1 )}{1 ^{2}}