The amplitude of sin (π/5) + i( 1 - cos (π/5))

Question

The amplitude of sin (π/5) + i( 1 - cos (π/5))  (A) (2π/5) (B) (π/5) (C) (π/15) (D) (π/10)

Tardigrade Admin · Accepted Answer

Let Z = sin (π/5) + i( 1 - cos (π/5)) Putting sin (π/5) =r cos θ ...(i) and 1 - cos (π/5) = r sin θ...(ii) ∴ : :: : tan θ = (1- cos (π/5)/ sin (π)5) = ( 2 sin2 (π/10)/2 sin (π)10 cos (π)10 ⇒ tan θ = tan (π/10) ⇒ θ = (π/10)

Q. The amplitude of $sin \frac{π}{5} + i (1 - cos \frac{π}{5})$

$\frac{2 π}{5}$

$\frac{π}{5}$

$\frac{π}{15}$

$\frac{π}{10}$

Q. The amplitude of sin5π​+i(1−cos5π​)

52π​

5π​

15π​

10π​

Let Z=sin5π​+i(1−cos5π​) Putting sin5π​=rcosθ ...(i) and 1−cos5π​=rsinθ...(ii) ∴tanθ=sin5π​1−cos5π​​=2sin10π​cos10π​2sin210π​​ ⇒tanθ=tan10π​⇒θ=10π​

Q. The amplitude of $sin \frac{π}{5} + i (1 - cos \frac{π}{5})$

$\frac{2 π}{5}$

$\frac{π}{5}$

$\frac{π}{15}$

$\frac{π}{10}$