What is the value of cos(-1/4 pi) ?

The value of cos(-1/4 pi) is (sqrt(2))/2

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cos(-1/4 pi)

cos (- \frac{1}{4} π)

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

cos (- \frac{1}{4} π)

Simplify:

- \frac{1}{4} π = - \frac{π}{4}

- \frac{1}{4} π

Multiply fractions:

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

= - \frac{1 π}{4}

Multiply:

1 π = π

= - \frac{π}{4}

= cos (- \frac{π}{4})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{4}) = cos (\frac{π}{4})

= cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{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}

- cos (π) - \frac{1}{2} sin (2) π^{2}

3 (0.5) + sin (0.5) - e^{0.5}

23 cot (56. 9^{\circ})

4 (cos (2))^{2}

\frac{( 100 ) ^{2} \cdot sin ( 2 ) 30}{9.8}