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

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

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cos(-(3pi)/4)+isin(-(3pi)/4)

cos (- \frac{3 π}{4}) + i sin (- \frac{3 π}{4})

- \frac{2}{2} - i \frac{2}{2}

Solution steps

cos (- \frac{3 π}{4}) + i sin (- \frac{3 π}{4})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{3 π}{4}) = - sin (\frac{3 π}{4})

= cos (- \frac{3 π}{4}) + i (- sin (\frac{3 π}{4}))

Use the following property:

cos (- x) = cos (x)

cos (- \frac{3 π}{4}) = cos (\frac{3 π}{4})

= cos (\frac{3 π}{4}) + i (- sin (\frac{3 π}{4}))

Simplify

= cos (\frac{3 π}{4}) - i sin (\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}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= - \frac{2}{2} - i \frac{2}{2}

arccos (\frac{0}{2})

\frac{5}{sin ( 1 2 ^{\circ} )}

sec (\frac{2}{3})

tan (3 \frac{π}{2})

cot (2 6^{\circ})

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