Is cos(-pi/4)= 1/(sqrt(2)) ?

The answer to whether cos(-pi/4)= 1/(sqrt(2)) is True

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prove cos(-pi/4)= 1/(sqrt(2))

prove

cos (- \frac{π}{4}) = \frac{1}{2}

True

Solution steps

cos (- \frac{π}{4}) = \frac{1}{2}

Manipulating left side

cos (- \frac{π}{4})

Use the negative angle identity:

cos (- x) = cos (x)

= cos (\frac{π}{4})

Expand

cos (\frac{π}{4}) : \frac{2}{2}

cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

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}

= \frac{1}{2}

We showed that the two sides could take the same form

\Rightarrow True

Is cos(-pi/4)= 1/(sqrt(2)) ?
The answer to whether cos(-pi/4)= 1/(sqrt(2)) is True