What is the value of 8(cos(90)+isin(90)) ?

The value of 8(cos(90)+isin(90)) is 8i

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8(cos(90)+isin(90))

8 (cos (9 0^{\circ}) + i sin (9 0^{\circ}))

8 i

Solution steps

8 (cos (9 0^{\circ}) + i sin (9 0^{\circ}))

Use the following trivial identity:

cos (9 0^{\circ}) = 0

cos (9 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 8 (0 + i 1)

Simplify

= 8 i

116 sin (4 5^{\circ})

- 3 cos (12 0^{\circ})

4 (sin^{2} (\frac{\frac{5 π ^{2}}{12}}{42 2}))

\frac{490 sin ( 13 5 ^{\circ} )}{sin ( 10 5 ^{\circ} )}

\frac{1}{3} (- 8 cos (\frac{π}{3}) - \frac{tan ^{2} ( \frac{π}{3} )}{2})

What is the value of 8(cos(90)+isin(90)) ?
The value of 8(cos(90)+isin(90)) is 8i