What is the value of 2cos(2*pi/4) ?

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2cos(2*pi/4)

2 cos (2 \cdot \frac{π}{4})

0

Solution steps

2 cos (2 \cdot \frac{π}{4})

Rewrite using trig identities:

cos (2 \cdot \frac{π}{4}) = 0

cos (2 \cdot \frac{π}{4})

Simplify:

2 \cdot \frac{π}{4} = \frac{π}{2}

2 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 2}{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

= 2 \cdot 0

Simplify

= 0

arctan (\frac{1.3}{7.7})

\frac{1}{cos ( 1 5 ^{\circ} )}

arctan (43)

sin (\frac{5}{26}) cos (\frac{1}{26})

\frac{4 cos ( 33 0 ^{\circ} ) + 2 sin ( 6 0 ^{\circ} )}{3}