What is the value of sqrt(3)(cos(pi/6)+i, pi/6) ?

The value of sqrt(3)(cos(pi/6)+i, pi/6) is sqrt(3)((sqrt(3))/2+i, pi/6)

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sqrt(3)(cos(pi/6)+i, pi/6)

3 (cos (\frac{π}{6}) + i, \frac{π}{6})

3 (\frac{3}{2} + i, \frac{π}{6})

Solution steps

3 (cos (\frac{π}{6}) + i, \frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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{3}{2}

= 3 (\frac{3}{2} + i, \frac{π}{6})

arcsin (\frac{309.4 \cdot sin ( 42.3 1 ^{\circ} )}{238.99})

arccos (0.999)

sin (42. 5^{\circ})

sin (0) \cdot sin (0)

8 \cdot 10 \cdot cos (15 0^{\circ})

What is the value of sqrt(3)(cos(pi/6)+i, pi/6) ?
The value of sqrt(3)(cos(pi/6)+i, pi/6) is sqrt(3)((sqrt(3))/2+i, pi/6)