What is the value of (cos(2pi)3^2)/4 ?

The value of (cos(2pi)3^2)/4 is 9/4

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(cos(2pi)3^2)/4

\frac{cos ( 2 π ) 3 ^{2}}{4}

\frac{9}{4}

Decimal Notation

2.25

Solution steps

\frac{cos ( 2 π ) \cdot 3 ^{2}}{4}

Rewrite using trig identities:

cos (2 π) = 1

cos (2 π)

cos (2 π) = cos (0)

cos (2 π)

Rewrite

2 π

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

= \frac{1 \cdot 3 ^{2}}{4}

Simplify

= \frac{9}{4}

sin (\frac{3}{3 2})

- 580 sin (2 6^{\circ})

tan_{- 1} (\frac{9}{4})

sin (2 (0.5)) + cos (2 (0.5)) + e^{- 2 (0.5)}

cos (7 0^{\circ}) 20