Question

The amplitude of `sin  pi/5 + i(1 - cos  pi/5)` is ______.

Options

• `(2pi)/5`

• `pi/5`

• `pi/15`

• `pi/10`

Answer 1

The amplitude of `sin  pi/5 + i(1 - cos  pi/5)` is `underlinebb(pi/10)`.

Explanation:

Here, rcosθ = `sin (pi/5)` and rsinθ = `1 - cos  pi/5`

Therefore, tanθ = `(1 - cos  pi/5)/(sin  pi/5)`

= `(2sin^2  (pi/10))/(2sin (pi/10).cos(pi/10))`

⇒ tanθ = `tan(pi/10)` i.e., θ = `pi/10`.