What is the value of cos((2pi)/3)-arctan(1) ?

The value of cos((2pi)/3)-arctan(1) is -1/2-pi/4

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cos((2pi)/3)-arctan(1)

cos (\frac{2 π}{3}) - arctan (1)

- \frac{1}{2} - \frac{π}{4}

Decimal Notation

- 1.28539 \dots

Solution steps

cos (\frac{2 π}{3}) - arctan (1)

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 π}{3})

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{1}{2}

Use the following trivial identity:

arctan (1) = \frac{π}{4}

arctan (1)

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{4}

= - \frac{1}{2} - \frac{π}{4}

cot (arccos (- \frac{2}{5}))

40 sin (7 0^{\circ})

58 sin (6 0^{\circ})

8 cos (5 1^{\circ})

e^{- c o s (0)}

What is the value of cos((2pi)/3)-arctan(1) ?
The value of cos((2pi)/3)-arctan(1) is -1/2-pi/4