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

The value of cos(2*pi/4)*pi/4 is 0

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cos(2pi/4)pi/4

cos (2 \cdot \frac{π}{4}) \cdot \frac{π}{4}

0

Solution steps

cos (2 \cdot \frac{π}{4}) \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

= 0 \cdot \frac{π}{4}

Simplify

= 0

cos (\frac{7 π}{9}) + tan (\frac{7}{15} π) sin (1 5^{\circ})

\frac{4.88 \cdot 1 0 ^{- 7}}{sin ( 1 ^{\circ} )}

arcsin (0.8238)

\frac{sin ( 7 5 ^{\circ} ) \cdot 7.35}{sin ( 3 5 ^{\circ} )}

tan (\frac{9 π}{10})