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

The value of cos(3(pi/4)) is -(sqrt(2))/2

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cos(3(pi/4))

cos (3 (\frac{π}{4}))

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

cos (3 (\frac{π}{4}))

= cos (3 \cdot \frac{π}{4})

Simplify:

3 \cdot \frac{π}{4} = \frac{3 π}{4}

3 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 3}{4}

= cos (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

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}

= - \frac{2}{2}

= - \frac{2}{2}

arctan (\frac{60}{30})

400 \cdot cos (6 0^{\circ})

4 (cos (4 5^{\circ}) + i sin (4 5^{\circ}))

arccos (\frac{18}{25})

2 cos (2 - π)