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

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

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cos(pi/4)-pi/4

cos (\frac{π}{4}) - \frac{π}{4}

\frac{2}{2} - \frac{π}{4}

Decimal Notation

- 0.07829 \dots

Solution steps

cos (\frac{π}{4}) - \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} - \frac{π}{4}

(\frac{3}{2}) (\frac{9.8}{0.4}) (1 - sin (6 0^{\circ}) + cos (6 0^{\circ}))

cos (0.68)

cos (15 0^{\circ}) - sin (24 0^{\circ}) + tan (30 0^{\circ})

arctan (\frac{- \frac{3}{2}}{\frac{1}{2}})

arccos (- 0.05)

What is the value of cos(pi/4)-pi/4 ?
The value of cos(pi/4)-pi/4 is (sqrt(2))/2-pi/4