What is the value of 8cos(-pi/4) ?

The value of 8cos(-pi/4) is 4sqrt(2)

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8cos(-pi/4)

8 cos (- \frac{π}{4})

42

Decimal Notation

5.65685 \dots

Solution steps

8 cos (- \frac{π}{4})

Rewrite using trig identities:

cos (- \frac{π}{4}) = \frac{2}{2}

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}

= 8 \cdot \frac{2}{2}

Simplify

8 \cdot \frac{2}{2} : 42

8 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 8}{2}

Divide the numbers:

\frac{8}{2} = 4

= 42

= 42

sin (14 0^{\circ}) cos (2 0^{\circ}) - cos (14 0^{\circ}) sin (2 0^{\circ})

tan (0 π)

arccos (0.69)

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