What is the value of 6cos(-pi/4) ?

The value of 6cos(-pi/4) is 3sqrt(2)

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6cos(-pi/4)

6 cos (- \frac{π}{4})

32

Decimal Notation

4.24264 \dots

Solution steps

6 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}

= 6 \cdot \frac{2}{2}

Simplify

6 \cdot \frac{2}{2} : 32

6 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 32

= 32

\frac{tan ( 7 3 ^{\circ} ) - tan ( 1 3 ^{\circ} )}{1 + tan ( 7 3 ^{\circ} ) tan ( 1 3 ^{\circ} )}

400 sin (4 5^{\circ})

arccos (\frac{3}{34})

\frac{2 tan ( \frac{2 π}{7} )}{1 - tan ^{2} ( \frac{2 π}{7} )}

10 sin (\frac{π}{6})