What is the value of 1+cos((3pi)/4) ?

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

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1+cos((3pi)/4)

1 + cos (\frac{3 π}{4})

1 - \frac{2}{2}

Decimal Notation

0.29289 \dots

Solution steps

1 + cos (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 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}

= 1 - \frac{2}{2}

sin (arctan (\frac{1}{2}))

2 sin (\frac{π}{8}) cos (\frac{π}{8})

arccos (cos (- \frac{5 π}{4}))

sin (12 7^{\circ})

1 - 2 sin^{2} (\frac{π}{8})

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