Express sin π/5 + i(1 – cos π/5) in polar form.

1.	Express sin π/5 + i(1 – cos π/5) in polar form.
Answer» Given as Z = sin π/5 + i(1 – cos π/5) On using the formula, sin 2θ = 2 sin θ cos θ 1 - cos 2θ = 2 sin² θ Therefore, Z = 2 sin π/10 cos π/10 + i(2 sin² π/10) = 2 sin π/10 (cos π/10 + i sin π/10) Thus, the polar form of sin π/5 + i(1 – cos π/5) is 2 sin π/10(cos π/10 + i sin π/10)

Answer»

Given as

Z = sin π/5 + i(1 – cos π/5)

On using the formula,

sin 2θ = 2 sin θ cos θ

1 - cos 2θ = 2 sin² θ

Therefore,

Z = 2 sin π/10 cos π/10 + i(2 sin² π/10)

= 2 sin π/10 (cos π/10 + i sin π/10)

Thus, the polar form of sin π/5 + i(1 – cos π/5) is 2 sin π/10(cos π/10 + i sin π/10)

Discussion