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

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

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-cos(pi/4)+1

- cos (\frac{π}{4}) + 1

- \frac{2}{2} + 1

Decimal Notation

0.29289 \dots

Solution steps

- cos (\frac{π}{4}) + 1

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} + 1

tan (\frac{1}{1})

2 sin (\frac{π}{4}) + 2 cos (\frac{π}{4})

arctan (\frac{12}{6})

arctan (\frac{12}{8})

sec (\frac{53 π}{8})